Question

How do you write an equation of an ellipse in standard form given center (-1, 3) vertex (3,3) and minor axis of length 2?

Answer 1

`(x+1)^2/16 + (y-3)^2/4 = 1`

Explanation:

The standard form for an ellipse is
`(x-h)^"/a^2 +(y-k)^2/b^2 = 1`
where `(h,k)` is the centre of the ellipse, `a` is the distance from the centre to the vertices and `c` is the distance from the centre to the foci. `b` is the minor axis.

`b^2+c^2 = a^2`

In this example `a = 3 - (-1) = 4` (The difference if the `x` coordinates of the centre and the vertex.)

The equations is `(x+1)^2/16 + (y-3)^2/4 = 1`