SOLUTION: Write this equation in standard form and find both the vertices and foci. 4x^2+4y^2-20x-32y+81=0

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Question 958093: Write this equation in standard form and find both the vertices and foci. 4x^2+4y^2-20x-32y+81=0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Write this equation in standard form and find both the vertices and foci.
4x^2+4y^2-20x-32y+81=0
complete the square
4x^2-20x+4y^2-32y=-81
4(x^2-5x+25/4)+4(y^2-8y+16)=-81+25+64
4(x-5/2)^2+4(y-4)^2=8
divide by 4
%28x-5%2F2%29%5E2%2B%28y-4%29%5E2=2
This is an equation of an circle with center at (5/2,4) and radius=√2
vertices and foci do not apply to circles, but in this case it is also a special case of an ellipse with eccentricity=1, which makes the ellipse a circle.
a^2=2
b^2=2
c^2=a^2+b^2=4
c=2
eccentricity=c/a=2/2=1