Question

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

Answer 1

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

Answer 2

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

Answer 3

To learn