Question

What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and co-vertices (9,1) and (−13,1)?

Answer 1

`((x+2)^2)/(121) + ((y-1)^2)/(169) = 1`

Explanation:

First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:

`((x-h)^2)/(b^2) + ((y-k)^2)/(a^2) = 1`

(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.

This gets us (-2, 1)

Therefore, h = -2, k = 1

Now we want to find a,

we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13

Now we want to find b,

We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11

Now we will just plug in all the values and simplify to get our answer! B)