Question

What are the coordinates of the center of the ellipse shown below?

(x+2)^2 (y-4)^2
------- + -------- = 1
9 36

(2,-4)

(-2,4)

(9,36)

(3,6)

Answer 1

when you write the ellipse in that form,

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

the center is at (h,k), and the axes are of length a and b

if a^2 > b^2, then it is horizontal, otherwise vertical if a^2 < b^2. if a^2=b^2 it is the special case of an ellipse known as a circle :-)

Answer 2

sorry, the semi axes...

Answer 3

so what do I do next?

Answer 4

well, all you have to do is compare your equation with the form I gave you, and read out the coordinates of the center

Answer 5

you have
(x+2)^2/9 + (y-4)^2/36 = 1

I have
(x-h)^2/a^2 + (y-k)^2/b^2 = 1

what is the value of h? what is the value of k? for extra credit, what are the values of a and b?

when you know h and k, you know the center is at (h, k)

Answer 6

-2,4?

Answer 7

a is 3 and b is 6

Answer 8

if h = -2, and k = 4, the center is at (-2, 4)

Answer 9

that was easy, right? :-)

Answer 10

yeah

Answer 11

Sometimes it is more complicated, and you have to do some algebra to get it into that form. For example, y^2 - 8y + 4x^2 + 16x - 4 = 0 is actually an equation for that same ellipse, but it sure isn't obvious, is it?

Answer 12

but by shuffling things around and completing the square on both x and y, you could get it into that same form we had and read out the center and semi-major/minor axes