Expert: Jack Cheng - 11/15/2006

Question
Hi. I have two question maybe you can help me?

1)  Write the polar equation of angle 45 degrees in rectangular form.


2) For the ellipse with equation 5x^2+64y^2+30x+128y-211=0  find the coordinates of the center, foci and vertices. Then graph the equation

If you could help me I will appreciate. Thank You

Answer
Hi Cana,

1) I am not very familiar with polar equations, but here's my three cents:

tan 45 = y/x   (in degrees)
1 = y/x
x=y

I hope my three cents help.

2) The equation for an ellipse is (x-h)^2/A + (y-k)^2/B = 1, and that's what you are working toward.

To convert 5x^2+64y^2+30x+128y-211=0, you'll have to put the x together, then the y, and complete the square for each. So:

5x^2+30x = 5(x^2+6x) = 5(x^2+6x+9-9) = 5(x+3)^2 - 45.
64y^2+128y = 64(y^2+2y) = 64(y^2+2y+1-1) = 64(y+1)^2 - 64.

Putting those back in, we have:

5(x+3)^2 - 45 + 64(y+1)^2 - 64 - 211 = 0
5(x+3)^2 + 64(y+1)^2 - 320 = 0
5(x+3)^2 + 64(y+1)^2 = 320    (dividing all by 320)
(x+3)^2/64 + (y+1)^2/5 = 1

That is the form that we want. You can probably find the vertex and foci with that (isn't center and vertex the same?).

I hope this helps,
Jack