SOLUTION: Find the equation of the ellipse described. Focus at (0, -3) and (0, 3) vertices at (0, 7) and (0, -7)

Question 854642: Find the equation of the ellipse described. Focus at (0, -3) and (0, 3) vertices at (0, 7) and (0, -7)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
With vertices at (0, 7) and (0, -7),
we know that the major axis is the vertical segment connecting (0, 7) and (0, -7),
and that the center of the ellipse is located at (0,0),
the midpoint of the major axis.
We also know that the semi-major axis will be
, the distance from the center to either one of the vertices.
We know that the focal distance is
, the distance from the center to the known focus.
We can find , the semi-minor axis by using the known relation

So -->-->-->
Since the equation of an ellipse centered at the origin, with a vertical major axis is

Since and our equation is

is Pythagoras applied to triangle .
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