How do you find an equation for the ellipse with vertices at (-6,4) and (10,4); focus at (8,4)?

1 Answer
Nov 16, 2016

Please see the explanation.

Explanation:

The equation of an ellipse:

(xh)2a2+(yk)2b2=1;a>b

Has vertices at (h±a,k)
Has foci at (h±a2b2,k)

Use the vertices to write 3 equations:

k=4 [1]
ha=6 [2]
h+a=10 [3]

Use equations [2] and [3] to solve for h and a:

2h=4
h=2
a=8

Use the focus to write another equation:

8=h+a2b2

Substitute values for h and a:

8=2+82b2

6=64b2

36=64b2

b2=6436

b2=28

b=28

Substitute the values into the standard form:

(x2)282+(y4)2(28)2=1