SOLUTION: Write the standard form of the ellipse 4x^2+y^2-2y=15?

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Question 968831: Write the standard form of the ellipse 4x^2+y^2-2y=15?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the standard form equation of an ellipse is
a. if the major axis of this ellipse is horizontal:
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1 where a%3Eb
b. if the major axis of this ellipse is vertical:
x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2=1 a%3Eb
the standard form equation for the translation(h,k) of an ellipse is:
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
you are given 4x%5E2%2By%5E2-2y=15
so, complete squares
4x%5E2%2B%28y%5E2-2y%2B_%29-_=15
4x%5E2%2F4%2B%28y%5E2-2y%2B1%5E2%29%2F4-1%5E2%2F4=15%2F4
x%5E2%2B%281%2F4%29%28y%5E2-2y%2B1%29-1%2F4=15%2F4
%28x-0%29%5E2%2B%281%2F4%29%28y-1%29%5E2=15%2F4%2B1%2F4
%28x-0%29%5E2%2B%281%2F4%29%28y-1%29%5E2=16%2F4
%28x-0%29%5E2%2B%281%2F4%29%28y-1%29%5E2=4.........both sides divide by 4
%28x-0%29%5E2%2F4%2B%281%2F4%29%28y-1%29%5E2%2F4=4%2F4
highlight%28%28x-0%29%5E2%2F4%2B%281%2F16%29%28y-1%29%5E2=1%29