An ellipse has its center at the origin, its foci on the y-axis, and its major axis is three times as long as its minor axis. Given that the ellipse passes through the point (-4,0), find its equation.

Express your answer in the form (x-a)^2/r^2 + (y-b)^2/s^2 = 1.

Thank you !!

Guest Nov 16, 2019

#1**+1 **

Since the ellipse is centered at the origin and its foci are on the y axis and it passes through the point (-4,0), then the minor axis must be 8 units long and the major axis must be 24 units long

So.....b = 8/2 = 4

And a = 12/2 = 6

So.....the equation of the ellipse is

x^2 y^2

___ + _____ = 1

4^2 6^2

x^2 y^2

___ + ____ = 1

16 36

Here's a graph : https://www.desmos.com/calculator/qdv0dposwj

CPhill Nov 16, 2019