Question 1169048: Please help me with this.Finding the equation of ellipse given the center (2,0),focus (2,6),eccentricity 2/3.
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
The center is half-way between the two foci and the foci lie on the major axis. So if the center is at (2,0) and one focus is at (2,6), the other focus is at (2,-6) and the major axis is on the line  , a vertical line.
The distance from the center to either focus is  , the distance from the center to a vertex on the major axis is  , and the distance from the center to a vertex on the minor axis is  . The eccentricity is 
These quantities are related thusly:  and  .
Once you have used the given data to calculate and , use the formula for an ellipse centered at ) where the major axis is on a vertical line to derive your desired equation:
^2}{b^2}\,+\,\frac{(y\,-\,k)^2}{a^2}\ =\ 1)
John
My calculator said it, I believe it, that settles it
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