Question

How do I find the equation of an ellipse with:
Vertices: (-7,10), (-7,-10)
Foci: (-7, square root of 19) (-7, - square root of 19)

I think the center is (-7,0) and a^2 is 49 I just don't know how to get c^2 so I cant get b^2

Answer 1

Looks like you label your a to be associated with the major axis (the axis containing the foci)
In that case:
b^2 + c^2 = a^2

b^2 + (√19)^2 = 7^2
b^2 + 19 = 49
b^2 = 30

so are correct about the centre, so

(x+7)^2 /30 + y^2/49 = 1

http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php