## Sunday, May 24, 2009

### First time to be the Scribe !

Hello Everybody ! As I wrote in the title,this is the first time am the scribe and I'm the last one in the scribe list.So may be in this post I can make some mistakes but don't laugh at me ok =)) !And then ...here we go:

First thing I want to tell you is there are Horizontal Ellipse and Vertical Ellipse .The Formula of the two Ellipses are different.

To sketch the Ellipse with one formula like this one :

First is the center of ellipse. We have(x-2)2 and (y+1) 2 →the coordinate of the center is (2,-1) or we can call the point C(2,-1)

Now, look at 9 and 16 . 9 <>2 and 16 is a2 .Then it’s a Vertical Ellipse(look at the formula of the Vertical Ellipse ).

b2 = 9 → b = 3 ; a2 = 16 → a = 4

Remember b2 + c2 = a2 so c2 = 16 – 9 = 7 → c = √7

Ok so now we have to find the foci . the way to find the foci is easy. Just take the coordinate of the center plus c value to find F1, take the coordinate of the centre subtract c value to find F2.But remember this is the Vertical Ellipse. For example if we have a center C(h,k) and we found c so F1=(h,k+c) and F2=(h,k-c)

But if it’s Horizontal Ellipse, we will have F1=(h+c,k),F2=(h-c,k) .I’ll show you an example later.....

Come back with the first question , we’ll have the point F1(2,-1+√7) and F2(2,-1-√7).Now let’s find the vertices . To find A1 and A in the vertical ellipse,A1=(h,k+a) and A2=(h,k-a). And B1=(h+b,k);B2=(h-b,k)

Then A1= (2,3),A2= (2,-5)

B1=(5,-1) ,B2= (-1,-1)

Major Axis = 2a = 8;Minor Axis = 2b = 6

Then we’ll have a “beautiful” ellipse like the picture below (I did’nt draw it) !

This is the Focal Radii Property:

So we'll have the formula :

Another question:

Sketch the Ellipse and find the coordinates of the center, foci and vertices with this one:

First is find the center just like the first question . We have C(-3,2)

Second, take a look at 25 and 16 . 25 > 16 → a2 = 25, b2 = 16 and it’s a Horizontal Ellipse.

→ a = 5 , b = 4

c2 = a2- b2 = 25-16 = 9 → c = 3

As I told you before, I’ll show you an example of the Horizontal Ellipse. And here is the formula :

F1=(h+c,k),F2=(h-c,k)

A1= (h+a,k),A2= (h-a,k)

B1=(h,a+k),B2=(h,a-k)

→F1=(0,2),F2=(-6,2)

A1=(2,2),A2=(-8,2)

B1=(-3,6),B2=(-3,-2)

Major axis = 2a = 10

Minor axis = 2b = 8

And sketch the ellipse ^^:

Standard form → General form → Back again :

The last thing I want to tell you is how to recognize the parabola, circle and ellipse :

If they give you one formula like this :

16x2 + 25y2 + 96x - 100y - 156 = 0

So this one is the formula of the parabola , circle or ellipse.

First, it’s cannot be the parabola because there are x2 and y2 ­in this formula and in the parabola, there is x 2 or y2 (just one of them).Second, there are same numbers in x2 and y2 with the circle(Ex: 16x2 and 16y2) but in this formula there are different numbers (16 and 25).So this one is the formula of an ellipse!

Ok so my mission is completed . Just remember to bring your paper with the circle and 30-35 points to our class tomorrow !