SOLUTION: Write the equation of the ELLIPSE that satisfies the given conditions Center (3,2) focus (3,7) vertex (3, -5)

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Question 1190961: Write the equation of the ELLIPSE that satisfies the given conditions
Center (3,2) focus (3,7) vertex (3, -5)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Center (3,2) ->h=3,k=2
foci (3, 7) -> b=7
vertex (3,-5) ->c=5
it has the transverse axis as the y-axis and its conjugate axis as the x-axis
The equation of an ellipse is
%28x-h%29%5E2%2Fb%5E2%2B+%28y-k%29%5E2%2Fa%5E2+=1
where (h,k) is the center, a+and b are the lengths of the semi-major and the semi-minor axes.

then a%5E2=7%5E2-5%5E2=24
%28x-3%29%5E2%2F24%2B+%28y-2%29%5E2%2F49+=1