Question

How do I write the equation of the conic section given this info?: An ellipse with the vertices `(0,-5)` and `(0,5)` and a minor axis of length 8

Answer 1

`x^2/16+y^2/25=1`

Explanation:

As the vertices are `(0,-5)` and `(0,5)` and length of its minor axis is `8`, the vertices must represent ends of major axis and hence length of its major axis is `10`.

Further center of ellipse is `(0,0)` and vertices are on `y`-axis and therefore major axis is parallel to `y`-axis and minor axis is parallel to `x`-axis.

Hence the equation of such an ellipse is

`x^2/(8/2)^2+y^2/(10/2)^2=1`

or `x^2/16+y^2/25=1`

or `25x^2+16y^2-400=0`

graph{(25x^2+16y^2-400)(x^2+y^2-10y+24.95)(x^2+y^2+10y+24.95)=0 [-12, 12, -6, 6]}