SOLUTION: How do I work my way through a math problem in finding the equation of an ellipse in standard form with vertices (2,-4) and (2,-10) and Foci 92,-5) (2,-9)?

Question 117685: How do I work my way through a math problem in finding the equation of an ellipse in standard form with vertices (2,-4) and (2,-10) and Foci 92,-5) (2,-9)?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
finding the equation of an ellipse in standard form with vertices (2,-4) and (2,-10) and Foci (2,-5) (2,-9)?
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Plot the points on a coordinate system so you can see what the ellipse
looks like.
----------------
Do you see the center is half-way from -4 to -10 or at (2,-7)
The semi-major axis is a = 3
Distance from center to focus is c = 2
---------------
For an ellipse a^2=b^2+c^2
So, 3^2 = b^2 + 2^2
b^2 = 5
b = sqrt(5)
----------------
EQUATION:
[(x-2)^2]/5 + [(y+7)^2]/9 = 1
===============
Cheers,
Stan H.
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