Question

An ellipse has a vertex at (5,0), a co-vertex at (0, -3), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

`(x^2)/(25)+(y^2)/(9)=1`

Explanation:

`((x-h)^2)/(a^2)+\frac[(y-k)^2}{b^2}=1`

her center
`(h,k)`, and
`a` is the horizontal radius, and
`b` is the vertical radius.

So the center is
`(h,k)=(0,0)`.

`a=5` because (5,0) has a distance of 5 from (0,0).

`b=3` because (0,-3) has a distance of 3 from (0,0).

So the equation is:

`((x-0)^2)/(5^2)+((y-0)^2)/(3^2)=1`

Simplifying a bit:

`(x^2)/(25)+(y^2)/(9)=1`