Question 857855: Find the equation in standard form of the ellipse with foci (0,5) and (0,-5) and major axis of length 14
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The foci are on the y-axis, so the vertices, and the major axis will be on the y-axis too.
With the foci at (0,5) and (0,-5), the center is obviously at (0,0),
the midpoint of the segment connecting the foci.
(When not so obvious, the midpoint coordinates are calculated from the coordinates of the foci, by averaging them,
 and  ).
The focal distance, the distance from either focus to the center is obviously  .
(When not so obvious, we calculate it as half the difference between the coordinates of the foci:
 ).
We calculate the semi-major axis  as half the length of the major axis:
 ,
The equation of an ellipse centered on the origin, (0,0),
and with the major axis along the y-axis is
 .
We need to find  , the square of the semi-minor axis  .
It can be found from  :
The equation of the ellipse is
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