What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)?Answer

What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)?Answer
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The foci lie on the major axis, so in this case the y-axis is the major axis, which has length 16. The formula f²=a²-b², where a=8 is the length of the semi-major axis and ±a is the y-coord of the vertices, allows us to find b, the length of the semi-minor axis (x-axis). We know f=4 so we can find b²=8²-4²=48. So the equation of the ellipse is y²/64+x²/48=1.

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