Question

Find the center of the circle given by this equation:

Answer 1

Answer:

center is (5,3)

Step-by-step explanation:

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