Last Minute BOB... probably won't count...

Haha so until today I had completely forgot about the math test I missed on Friday and realized when i arrived at school today that I would be doing this test today. SO i decided I should write my BOB now... it may not count cuz oif the super lateness of it, but I'm gonna do it just in case.

All right, so Conics is one crazy unit. Started out learning about the ancient Japanese art from Samurai Kuro Pat Wa and all the different shapes you can form from cutting a cone. A cone is basically if you took a line and just spun it around. From here you can cut out 4 shapes. You can cut out a circle, an ellipse, a parabola, and a hyperbola. Each one is different.

Some commonalities include:

• Vertices
• Foci
• Focal Radii
• Locuses (Loci?) of points

Equations to remember~

Parabola:

• (x-h)^2=4p(y-k) (vertical parabola)
• (y-k)^2=4p(x-h) (horizontal parabola)
• (h,k)=Vertex
• p=distance from vertex to directrix or a focal point

Circle:

• (x-h)^2+(y-k)^2=r^2
• r=radius
• (h,k)=center

Ellipse:

• ((x-h)^2/a^2)+ ((y-k)^2/b^2)=1 *horizontal*
• ((y-k)^2/a^2]+[(x-h)^2/b^2)=1 *vertical*
• a=semimajor axis
• b=semiminor axis
• c= distance from center to foci
• (h,k)=center

Hyperbola:

• ((x-h)^2/a^2)-((y-k)^2/b^2)=1 *horizontal*
• ((y-k)^2/a^2)-((x-h)^2/b^2)=1 *vertical*
• a= transverse axis
• b= conjugate axis
• c= distance to foci
• (h,k)=center

My struggles:

• Have had some trouble in identifying vertical/horizontal in some instances.
• Sometimes get confused between the ellipse and hyperbolic equations.
• Issues with completing the square.

But I have done some looking over things this weekend and, all in all, this un it is not extremely difficult and so hopefully I will do quite well on it. Next period here I come!

~ Pokemon Champion

BOOOOOBBBB!!!!!!

lol Hey Everyone
Well this unit has practically zoomed by and, for me, has been the easiest unit of them all. It was made especially easy by the fact that there were only a very small number of formulas to memorize and a lot of graphs and patterns. The only thing I really need to remember for these is how to find the focuses on ellipses and how to graph a hyperbola.

Ellipses
take the square root of the difference between the semi-major axis squared and the semi-minor axis squared. this is how far, along the major axis, the foci's are from the center.

Hyperbola
first you need to draw the box created by the conjugate and semi transverse axises. from there you can draw the diagonal lines that make up the asymptotes of the hyperbola. Each one intersects the two opposite points on this box that has been created. Now take the lengths of the conjugate axis and the semi-transverse axis. Now square both of them and add them together. Then take the square root of that to find the distance between the centre and one of the foci's.

Well that is practically everything that I can think of at the moment so Wish Me Luck!!
See you guys in class.

Jessi

Long Distance BOB....Will You Accept The Conic Charges?

LOL well ok, it's not really long distance. But I just came back from Kenora so I thought that would be appropriate. It's great to be back home (although I do miss the bus and the hotel a bit).

Man this unit just zoomed by! It's making me realize that in a couple weeks, I, along with the rest of us grade 12 math takers, will be taking the provincial exam for math. (I'm kinda nervous but I think I'll pull it off. :D)

I'll have to admit that at first, Conics sounded really intimidating. For me, it was because we had to deal with graphing parabolas/circles/hyperbolas/ellipses and see the patterns that accompany them and I really dislike parabolas and graphing them. I'm more of a problem solver and equation person. I guess as the unit went on, a lot of the stuff came pretty easy to me and the unit became easier. I learned to recognize the patterns easily and pull off a "Matrix"-esque move in math. We all learned how to do that didn't we? I think that's pretty awesome.

The easiest part of this unit was learning the different patterns and remembering what stood for what in each equation. I may not remember a lot of things, but for some reason, I do remember things relating to math fairly well. I also felt that how and why the equations worked was pretty interesting. 8)

The hardest part of this unit was the word problems. It's only because I end up thinking about the wrong things, but then again that might just be a coincidence. Hopefully, with the practice I took today with those types of problems, I'll be able to conquer them with ease. Graphing wasn't as hard as I thought it would be, but it was a pain (but that's just me being lazy xD).

I feel that there's only a couple things I need to remember for this test. One of these things being the pictures relating to the parabola/circle/ellipse/hyperbola showing how each parameter relates to the other. The second of these things being the equations for each of the conic chapes.

Parabola:
(x-h)²=4p(y-k) [vertical]
(y-k)²=4p(x-h) [horizontal]
(h,k)=Vertex
p=distance from vertex to directrix or vertex to focus point

Circle:
(x-h)²+(y-k)²=r²
r=radius
(h,k)=center

Ellipse:
[(x-h)²/a²]+[(y-k)²/b²]=1 {horizontal}
[(y-k)²/a²]+[(x-h)²/b²]=1 {vertical}
a=semimajor axis
b=semiminor axis
(h,k)=center

Hyperbola:
[(x-h)²/a²]-[(y-k)²/b²]=1 {horizontal}
[(y-k)²/a²]-[(x-h)²/b²]=1 {vertical}
a= transverse axis
b= conjugate axis
(h,k)=center

If I remember all this stuff, I think I'll do fine. I really am not too worried about this test.
Well, I guess that's all? I will see you all tomorrow! If you ahven't seen the intro to our (Dion, Mary, me) DEV yet, you can view it by clicking the link in the previous post (which should be very short :D). Hopefully, our DEV will be able to fulfill your expectations after watching the intro.

pc

~jayp~

BOB on Conics

Heeey everybody, sorry to say that this will be short and sweet because I've got loads to do tonight unfortunately :<

On with my BOB!
Honestly, this unit sounded intimidating, but in the end, it really wasn't at all! After I got past getting the hang of the geometry, I actually started to enjoy it... (Except for sketching graphs, I always did despise doing that.) :]
So now that I pretty much get the jist of all the geometry involving parabolas, ellipses and hyperbolas, I think I'll do well in that aspect.
However...
Applying them to "realistic" situations won't be my cup of coffee (gonna have to load up on this tmrw huhu). I'm sure with a little more practice I'll have a full understanding of taking pieces of information and constructing the proper equation for it, but waugh! In due time...

What I found interesting was that when you take a line and "spin" it, you end up with two cones, and from there you can derive the parabola, ellipse, and hyperbola! I'd describe/post images of this, but Jessi's scribe post on Conics had very good ones already :].

Now, onto the guidelines which I shamefully hardly ever follow...

• Get at least some sleep! Actually, sleep immediately after you study, you'll remember your stuff better!
• Eat breakfast, brain food = awesome because you don't want to hear your stomach during the test and neither do we lol.
• Take your time, don't rush!
• Keep in mind the equations for vertical/horizontal parabolas, ellipses, and hyperbolas!
• Look at these equations and see the geometry! Remember, "codes!"
• a^2 + b^2 = c^2!
• Be able to take very little given information and build upon them to end up with an equation that will help you out big time!

Anywhoots, I think that's enough brain juice spillage for me. Onto studying!
To everyone who's going on that Kenora trip tmrw... Bye. >_> Just kidding, have fun!
To everyone else, good luck on the test tmrw! :D

BOB for Conics

This unit was extremely short but I learned alot about it. this unit involved graphs like the parabola, ellipse, circle and hyperbola. In order to get these different types of graphs we can cut a double-sided cone( looks like an hour-glass) from different angles. If we cut the top it will create a circle. If we cut at an angle we can create an ellipse. If we cut the bottom it will create a parabola. and also if we cut it at a 90 degree angle down it will create a hyperbola.

The most interesting thing I learned and most useful was the anatomy of the Hyperbola.
This mini box allows us to find the hyperbola with ease and with less information required. Like if you have the conjugate axis and transverse you can find everything else like the asymptotes, vertex and center. Or if you have the slope of the asymptote and know the coordinates of an axis then you can find all the rest of the information also. Hyperbolas involve the difference of distances will always be constant.

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2)

+ or - determines whether its vertical or horizontal. Positive x = horizontal, negative x = vertical.

The ellipse was quite interesting. I was quite amazed that it does not have a radius but instead foci that help determine the value of c. Also within it are the major axis and minor axis. Which help determine the value of a and b in the standard form equation:

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)

the a and b's are switched in a vertical ellipse.

All in all it was short, but very straight forward. Mr.K said we should see the geometry when we see the equations like in the matrix where it shows code but they see people. I can safely say I'm ready and hope they're no big surprises.

Bobing for conics

ha ha made a mistake there =P
k for this up coming test i made sure to keep an eye out on the hyperbola because i thought that it might be the hardest in the conics unit.
-hyperbola is identified by having both x^2 and y^2 and is the difference between the two
-opens vertically if y is positive and horizontally if x is positive
-finding the foci is found by add the square of the minor transverse axis and minor conjugate axis. Like a^2 + b^2 = c^2
The rest of the conics; circle, ellipse, and parabola I'm gonna go over some more.
Best of luck guys for tomorrow!
Oh one last thing i just remembered about conics, remember the pattern i think or the geometry of the object in order to give yourself a picture.
I believe that's what I'm trying to say...
ha ha well good luck again!

BOB

This was really a quick unit! I understood that it's just really comprehending what the equation is telling you. The equations have been posted a lot of times here so i won't list them here on my BOB. Anyway, here are some random things that are to be noted:

1. The general equation of a conic is .

2. Completing the square is done to convert an equation's general form to standard form.

3. An ellipse has two axes of symmetry: the major axis and the minor axis.

4. If a hyperbola is parallel to the x axis, then x^2 is positive. If it is parallel to the y axis, then y^2 is positive.

5. (h,k) is the center of the conic.

6.a is the transverse axis in a hyperbola, while b is the conjugate axis. they indicate whether the hyperbola will be opening up and down, or left and right.

7. A parabola has only one variable squared, unlike the other ones.

Okay, good luck to everyone on the test! I know we'll all do well on it. :)
Night!

BOB not just sweet words

Reflection time again!!! I think that I'm current a very messed up canvas. It's not that I don't understand, I do but its just when it come test time that I feel that I don't. Everyone already posted most of the stuff you need to know and it will just be redundant if i say the again.

Success for the test(?):
- remember the formulas/equations!
- when we see the equations were suppose to see the graph!
- completing the square
- practice makes close to perfect
- eat, sleep and study
- confidence!

Good luck on the test tomorrow, study, study study.

-jennifer

bob

still reviewing for tomorrow.
I was on this net to review
http://webct.merlin.mb.ca/webct/urw/lc4130001.tp0/cobaltMainFrame.dowebct
i didn't find the foci, and how you solve that part.
I still didn't get the foci, and i think I'm good with other stuff.
good luck guys!!!!!

BOB

Hi. Here's my reflection on this unit:

I actually found this one interesting, since it felt cool when I successfully completed a question that asked me to graph something. Makes me feel like some kind of pro artist. :P Anyways, I struggled a little in the beginning. -Not- because it was hard, but because of some other issues that were affecting my work ethic.

I'm fairly confident about this test. I'm hoping to to get atleast 50% on it (just the passing. :P) but if I do better, then boo yeah. And yeah, I know I should "aim higher", but I'm just being realistic.

I won't bother going over anything, since everyone else probably will be doing it. (And better, I might add.)

Good luck on the test tomorrow.

-ConstantEcho

BOB on Conics

This is Jonno doing my BOB on our Conics unit before the test.

So, this unit was mainly about circles, parabolas, ellipses and hyperbolas...
For each of the stated above, we learned that each of them comes from a line that is spinned in a circle, basically, forming two cones. Depending on how you slice it, you can get one of the shapes/graphs/etc, stated above. We also learned the equations for each of the stated above. After Mr. K's talk about the matrix and such, he said we should also be able to identify what it is and what it looks like just by looking at the "code" or equation. I tagged a delicious link that can help you with this a bit, so if you're interested here it is!

Basically:
Parabolas - only have one squared term (ex. x^2 + y = 1)
Circles - have 2 squared terms that have equal coefficients (ex. x^2 +y^2 = 1)
Ellipses - hav 2 squared terms whose coefficients are not equal (ex. 2x^2 +y^2 = 1)
Hyperbolas - (I'm not 100 percent sure because i wasn't here for class that day, but from what I've seen...) have two squared terms, one being positive and one being negative? (ex. x^2 - y^2 = 0).

Another thing we learned was to change equations to general form from standard form and vice-versa.

I'm pretty sure i covered most of what we learned. I know there's more stuff, like the pythagorean theorum and such being used in the ellipse and hyperbola graphs, but I don't think I currently have enough skills to explain it.

What i found hard (until today) was finding the asymptote lines of the hyperbolas, but Mr. K. cleared that up for me.

Well, that's all I'm going to put up for my BOB.
Good Luck on the test everyone!

Jonno- Out

BOB

Hey there. This recent unit we did was conics. It was all about cones and stuff. I found this to be pretty simple, just like the stuff we did in grade 11 pre cal with parabolas.
there is a little diagram of how the shapes were formed.


Circle formula:
Elipse formula:
Parabola formula: or horizontal parabola:
Hyperbola formula:

I hope everyone gets an A+! don't forget about DEV projects

Conics BOB~

The conics section is one of my favorites. There weren't any big surprises and it seemed "short and sweet".

What we learned:

Parabolas

• vertex (h,k), a directrix (straight line, fixed distance from vertex), and focus(fixed distance from vertex)
  
• Standard form VERTICAL:

• Standard form HORIZONTAL:

• When 4p, also known as a, is greater than 1 the parabola is wide.
• When 4p is less than 1 the parabola is skinny.

Circles

• focus= center (h,k)
• Standard form:
• remember, the r is squared.

Ellipses

• center (h,k), Vertices's (endpoints on Major axis), major axis (length of 2a), semi-major axis (length of a, center to one of the vertices's), Minor axis (legnth of 2b), Semi-minor (length b),Foci (c units from center), Focal radi (distance b/w Foci and point on ellipses.
  
• The midpoint of two foci would center of ellipses.
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• a^2 is the bigger number.
  
• c^2 = a^2 - b^2

Hyperbola

• center (h,k), Transverse axis (the distance b/w the vertices's, which are also the vertex. Is the difference of foci to pt, foci2 to pt. length of 2a), semi-transverse axis ( a),conjugate axis (length of 2b), Sem-iconjigate (b), Foci (c units from center), asymptotes.
  
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• c^2 = a^2 + b^2
• When given slope of asymptotes, you can figure out the value of b or a. b/a = rise over run.

When changing equation from general to standard, you'd need to complete the square.

study hard guys!

BOB likes to eat icecream [cones]

I feel pretty confident for the test tomorrow, I might not get 100% but I believe I'll do better than what I have been doing so far. I liked this unit because it was pretty straight forward and I had no real trouble understanding any concepts.

I think that for this unit I just need to make sure I know the formulas really REALLY well. Let's review shall we ^__^

A PARABOLA:
The equations:

If the x is squared, the parabola is vertical (either opens up or down) and if the y is squared the parabola opens horizontally (opens left or right). p is the distance from the vertex to the directrix and the focal point. If 4p is a big number, the stretch of the parabola is also big. If the number is smaller than one the parabola will be skinny.

A CIRCLE:
The equation:


r is the radius. In general form, the coefficients of x and y are squared and are the same. That's how you know it's a circle!

AN ELLIPSE:
The equations:

When a (the bigger number) is under x, the ellipse is horizontal. If it's under y then its vertical.
a is the length of the semi major axis. b is the length of the minor axis. Use c^2 = a^2 - b^2 if you have to find the distance between the origin and the focal points. In general form, the coefficients for x and y are different.

A(N) HYPERBOLA:
The equations:


When x is positive the hyperbola is horizontal (opens right and left). When y is positive it is vertical (up and down). a is the length of the semi transverse axis, while b is the length of the semi conjugate axis.

use c^2 = a^2 + b^2 to find c, the distance from the origin to the focal points.

hyperbola graphs have asymptotes! use the slope formula to figure out their equations.

To be alright for the test, all we need to know are the formulas and how to graph them. I'm sure everyone will do fine! ;D

Make sure to eat healthy, drink plenty of water and get some rest so you can be in top shape tomorrow morning!

~Bye bye! :D

BOB for Conics

hi everybody, one more unit is done and i was almost forget about the BOB for this unit. T_T .
Anyhow, i just do this BOB briefly.

I think this unit is not really, you just need to know the formula and understand the graph so you could know which formula is parabola, ellipse, or hyperbola.

About the formula, i think some of us already posted it, so i am not going to repeat it. :D

Anyway, Good luck all guys, test on Friday and don't forget your delicious link [which i also almost forgot :-"] ...

BOB BOB BOB BOB :)

Hey everyone!
This unit went by really fast, and since it's the end of the school year, I'm becoming more lazy, so that means that I really haven't been paying much attention to a lot of things happening in class. So I really need to study a lot and make sure I do well on this test! The only thing I really need to review is the day when we learned about graphing parabolic equations since I wasn't in class for that lesson. I have a feeling it's not a hard thing to pick up, so hopefully I learn everything I need to know before our test, which is on friday. Other than that, I think I'll be okay. I'll just have to read through the slides to refresh my memory, and hope that I do well. I guess that's all, good luck! :)

BOBS on Conics?

Well this unit was relatively easy for me. The only things I think I will have problems with is reading the question properally and putting it in the right way.


So the first thing we learnt about was parabolas. We learnt another formula for a parabola which is :


P is the distance from your foci to your vertex or your distance from your directrix to your vertex.

If you want the horzontal graph, you just switch the (x-h) and (y-k).



The next thing we learned was circles and the formula is the same as the one we learned before so I'm not going to go into detail with that.



Then comes the elipses with the formula:

Where "a" is the length of the semi major axis and "b" is the semi minor axis.

If you want the vertical graph you just exchange the "a" and "b"

Then there's hyperbolas (parabolas on steriods, according to Mr. K)

Where "a" is your semi transverse axis and "b" is your semi congurant axis. If you want your vertical graph you just make "x" negative instead of "y".

So that's basically the simple summary of what we learn, time for my nap. Night.

Reflection on Conics

Well that was a quickfast unit. I found it so much easier than any of the previous units. :) But lately I've been lazy sooo... I need to get back with the program and practice, practice, practice! >_< Oh and I still need to look over the formulas a few times to make sure I don't mix them up. Remember that the transverse axis connects the two vertices of the hyperbola and can be either horizontal or vertical.

Good luck to everyone!

Is it a parabola? is it an ellipse? no its.. BOB

Well this unit was pretty short and sweet and fairly simple. I'm going to get right into a review because I've got to work on DEV.

##############################################

A parabola is a locus of points a fixed distance from a fixed point (focus) and a line (directrix).

Vertical Parabola: (x-h)^2=4p(y-k)

Horizontal Parabola: (y-h)^2=4p(x-k)

The coordinates (h,k) are the vertex of the parabola. "p" is the distance from the vertex to the focus or the vertex to the directrix.  These distances are both equal. When 4p is greater than one, the parabola is wider and when it is less than one, the parabola is narrower.

##############################################

A circle is the locus of points equidistant from a fixed point, the center and the distance to any one point is called the radius.

Circle: (x-h)^2 + (y-k)^2= r^2

The coordinates (h,k) are the vertex of the circle. "r" is the radius of the circle.

##############################################

An ellipse is the locus of points which the sum of the distances to the foci is known.

Horizontal Ellipse: [(x-h)^2/a^2] + [(y-k)^2/b^2] = 1

Vertical Ellipse: [(y-h)^2/a^2] + [(x-k)^2/b^2] = 1

In an ellipse addition is used because the locus of points is the sum of the distances. The center of the ellipse is the coordinates (h,k) and is halfway between the two foci. The semi major axis is equal to "a" and the whole major axis is equal to "2a". The semi minor axis is equal to "b" and the whole minor axis is equal to "2b". The distance of either foci to the center is distance "c" and can be determined by c^2=a^2-b^2.

##############################################

A hyperbola is the locus of points which the difference of the distances to the foci is known

Horizontal Hyperbola: [(x-h)^2/a^2] - [(y-k)^2/b^2] = 1

Vertical Hyperbola: [(y-h)^2/a^2] - [(x-k)^2/b^2] = 1

The transverse axis is the distance between the vertices of the hyperbola. This is distance "2a". The distance from either vertex to the center is "a" and is the semi transverse axis. The conjugate axis is perpendicular to the transverse axis and it's distance is "2b". Half the distance, "b", is called the semi conjugate axis. The distance of the foci can be calculated c^2= a^2+b^2.

##############################################

Well that is all so I'm to work on DEV! I hope everyone did well on the test!

 

BOB

Hi everybody its Alex, hope you're all doing WonderfullyExcelent. I have to admit that I don't feel very confident going in to this test. I found that I missed a lot of days and that we didn't do as much practice problems in class. Usually these practice problems help me a lot, but this unit I didn't feel there were enough of them. I understand that we are pressed for time so I'm not complaining.

I know we have to know about ellipses and hyperbolas and that we need to know how to graph them, but I feel that there are going to be a lot of problems on the test that will require us to use our indepth knoweledge of these ellipses and hyperbolas, that I just won't know. I'm expecting a test that will be very tricky for me, with lots of curve balls coming from no where.

I hope that I and my fellow class mates can get enough studying in to do WonderfullyExcelent on this test, and I hope everyone has more knowledge than me on this unit going into this test.

Best of Luck! Alex.