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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 !!

 Nov 16, 2019
 #1
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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

 

 

 

cool cool cool

 Nov 16, 2019

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