How do you find the equation in standard form of an ellipse that passes through the given points: (-8, 0), (8, 0), (0, -4), (0, 4)?

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Answer 1 · 2016-12-21T14:49:07

The equation is #x^2/64+y^2/16=1#

We use the equation the standard ellipse as the center is #(0,0)#

#x^2/a^2+y^2/b^2=1#

Let's take the vertex #(8,0)#, then

#64/a^2+0=1#, #=>#, #a=8#

Let's take the vertex #(0,4)#, then

#0+16/b^2=1#, #=>#, #b=4#

The equation of the ellipse is

#x^2/64+y^2/16=1#

graph{x^2/64+y^2/16=1 [-12.66, 12.65, -6.33, 6.33]}