Question

Find the center of the circle given by this equation:

Answer 1

center is (5,3)

Explanation:

`x {}^(2) - 10x + y {}^(2) - 6y - 30 = 0 \\ x {}^(2) - 10x + y {}^(2) - 6y = 30 \\ add \: \: \: 25 \: \: and \: \: 9 \: oneach \: side \: to \: make \: perfect \: square \\ x {}^(2) - 10x + 2 + y {}^(2) - 6y + 9 = 25 + 30 + 9 \\ (x - 5) {}^(2) + (y - 3) {}^(2) = 64 \\ (x - 5) {}^(2) + (y - 3) {}^(2) = 8 {}^(2)`