Question

Need help with ellipse
Find the equation of the ellipse with the following properties.

The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).

Find the equation of the ellipse with the following properties.

The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).


Find the equation of the ellipse with the following properties.

The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).



help help help!!!!!!!!!!!!!

Answer 1

The center of the first one is what?

Answer 2

It doesn't say

Answer 3

You should be able to figure it out by looking at the x intercepts and the y intercepts.

Answer 4

Mr. Ick:

"Find the equation of the ellipse with the following properties.

The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4)."

I'd suggest you graph these four intercepts and draw a rough ellipse through them. This will immediately give you visual idea of where the center of the ellipse is.

Which distance is greater? That from (-2,0) to (2,0) or that from (0,-4) to (0,4)?

the longer distance is on what we call the "major axis."

Answer 5

A general equation for an ellipse is

2 2
x y
--- + ---- = 1.
2 2
a b

I mentioned "major axis." "a" is the distance from the center to vertex along the longer axis. "b" is the distance from the center to vertex along the shorter axis.

Simply substitute those values into the equation above and you'll have your equation of the given ellipse.

If not clear: Please form questions and ask them.