SOLUTION: find the equation of the ellipse with vertices(0�8) and foci (0�5)

Question 1037772: find the equation of the ellipse with vertices(0�8) and foci (0�5)
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
Since the vertices are (0,8) and (0,-8), you know that this ellipse is centered around the origin.
The foci of an ellipse are always along the major (longer) axis. By the points given, you know the foci reside along the Y axis. So this ellipse is taller than it is wide.
The general equation for an ellipse that is taller than it is wide is of the following form:
((x-h)^2/b^2))+((y-k)^2/a^2))=1
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Since this ellipse is centered about the origin, h=k=0.
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We know a=8 since that is given
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So we need only to find b^2 to have all the terms of the equation.
Note that F is the term given to the distance from the center of the ellipse to each focus. So F=5.
A key equation of an ellipse allows us to find b:
F^2=a^2-b^2
25=64-b^2
-b^2=25-64
b^2=39
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Know you have everything you need to write the equation:

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Good Luck,
tutor_paul@yahoo.com

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