Posted by **sue** on Thursday, December 30, 2010 at 4:12am.

Find a Parabola with Vertex (3,1) Focus (4,1)

Find the vertex of 4y^2+4y-16x+13=0

Find the center of an ellipse 9x^2+4y^2-36x-24y-36=0

Find an ellipse with minor axis of 8 and vertices at (-9,3),(7,3)

- precal help -
**Damon**, Thursday, December 30, 2010 at 5:57am
In all of these problems complete the square, then look at standard form of conic section.

For example to find the center of the ellipse

Find the center of an ellipse 9x^2+4y^2-36x-24y-36=0

9 x^2 -36 x -36 = -4 y^2 + 24 y

(-9/4) x^2 + 9 x + 9 = y^2 -6 y

(-9/4) x^2 + 9 x + 18 = y^2 -6 y + 9

(-9/4) x^2 + 9 x + 18 = (y-3)^2

x^2 - 4 x - 8 = (-4/9) (y-3)^2

x^2 - 4 x = (-4/9) (y-3)^2 + 8

x^2 - 4 x + 2 = (-4/9) (y-3)^2 + 10

(x-2)^2 + (4/9) (y-3)^2 = 10

You can see right now that center is at (2,3)

(x-2)^2/10 + (y-3)^2/(90/4) = 1

- error -
**Damon**, Thursday, December 30, 2010 at 6:00am
x^2 - 4 x = (-4/9) (y-3)^2 + 8

x^2 - 4 x + 4 = (-4/9) (y-3)^2 + 12

(x-2)^2 + (4/9) (y-3)^2 = 12

You can see right now that center is at (2,3)

(x-2)^2/12 + (y-3)^2/(27) = 1

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