SOLUTION: Find the center and the foci of the ellipse 5x^2+12y^2-30x+24y+7=0

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Question 787615: Find the center and the foci of the ellipse
5x^2+12y^2-30x+24y+7=0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center and the foci of the ellipse
5x^2+12y^2-30x+24y+7=0
5x^2-30x+12y^2+24y=-7
complete the square
5(x^2-6x+9)+12(y^2+2y+1)=-7+45+12
5(x-3)^2+12(y+1)^2=50
divide by 50
(x-3)^2/10+12(y+1)^2/(50/12)=1
(x-3)^2/10+12(y+1)^2/(25/6)=1
This is an equation of an ellipse with horizontal major axis
Its standard form: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, a>b, (h,k)=(x,y) coordinates of center.
..
For given ellipse:
center: (3,-1)
a^2=10
b^2=25/6
c^2=a^2-b^2=10-25/6=35/6
c=√(35/6)≈2.42
foci:(3±c,-1)=(3±2.42,-1)=(0.58,-1) and (5.42,-1)