Question

Write the equation of the conic section with the given properties:
An ellipse with vertices (0, -5) and (0, 5) and a minor axis of length 8.

Answer 1

Do you recall the standard form equation for an ellipse.?

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

Answer 2

This looks familiar to me, yes.

Answer 3

That is an ellipse, centered at point (h,k), and
has axis lengths, a and b

Answer 4

Right, I believe the minor axis is 2b. So 8/2 = 4. 4 * 4 = 16. Would that be correct?

Answer 5

The major axis length is given by (0,-5) and (0,5) in the y-direction, this distance is 10
The minor axis is given by total length 8. From the origin it extends out 4 units in the x directions