Find the centre and radius of a circle 36x^2+24x+36y^2-36y-23=0

3 answers

To find the center and radius use the formula for the equation of a circle (x-h)^2 + (y-k)^2=r^2 where (h,k) is the center. and then solve for r by plugging in a point for x and y with using the center for h,k

btw find the equation by factoring and completing the square if necessary
No need to solve for r. Follow the hint and complete the squares.
36x^2+24x+36y^2-36y-23=0
36(x^2+2/3 x) + 36(y^2-y) = 23
36(x^2 + 2/3 x + 1/9) + 36(y^2 - y + 1/4) = 23 + 36/9 + 36/4
36(x + 1/3)^2 + 36(y - 1/2)^2 = 36
(x + 1/3)^2 + (y - 1/2)^2 = 1
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