First we found out why all of our satellites have the shape like it has nowadays. and the receiver is built at the focus of the parabola so wherever the radio rays, the GPS rays or any rays go, it will bounce in and intercept at the receiver which is the focus of the parabola.
Then we just quickly went over what we learned yesterday which are the formula of the vertical and horizontal parabolas. These formula is totally different but it actually the same with what we've learned before.
Just remember:
-When you see the x side square, it is the vertical parabola, if p is positive, then parabola opens up and if p is negative, the parabola opens down.
-When you see the y side square, it is the horizontal parabola, if p is positive, then the parabola opens to the right and if p is negative, the parabola opens to the left.
After that, we tried to solve the problem with this equation:
First thing we can easily see that there is a square in the y side so this i a horizontal parabola so we use this formula : (y-k)^2 = 4p(x-h)
and we can find the vertex with the coordinates (h,k) = (3,-1)
we also see that 4p = -8 so p must equals -2.
p is negative so the parabola opens to the left and the distance between the focus to the vertex and the vertex to the directrix is 2.
there is a question about how wide is the arms of the parabola?
we can see that the arms of the parabola intercept at the horizontal line which is x=0
we let x=0 and sub it into the equation. so i got
(y+1)^2 = -8(-3).
Then i expand the (y+1)^2, i got
y^2 + 2y + 1 = 24
subtract 24 from both side
y^2 + 2y - 23 = 0
then we factor it out and one solution is 3.8989... (approx 4) and one is -5.8989... (approx -6) so that is the wide of our parabola.
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We learned how to convert a standard form to the general form [ expand the equation ] and from the general form to the standard form [ complete the square ].
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We moved on with the circle.
we pick a point F to make the center of the circle, then draw a bunch of spots that have the same distances from the point F.
Use the distance formula, we found out the equation of the circle, just like what we did with the parabola.
And we solved the next problem about find the radius and the coordinate of the circle.
for this problem, we just complete the square to get the equation like the circle equation so we get the coordinate of the center. With the radius, remember to take the square root.
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Remember to do the homework, Generating ellipses.
Last thing is the next scribe is yíＮＡЙ
