Question

Help center of circle

Answer 1

Center = (7, - 5)

Radius = 3

Explanation:

`{x}^(2) + {y}^(2) + 14x - 10y + 65 = 0 \\ {x}^(2) + 14x + {y}^(2) - 10 + 65 = 0 \\ ( {x}^(2) + 14x + {7}^(2)) - {7}^(2) + ({y}^(2) - 10y + {5}^(2)) \\- {5}^(2) + 65 = 0 \\ (x + 7)^(2) + (y - 5)^(2) - 49 - 25 + 65 = 0 \\ (x + 7)^(2) + (y - 5)^(2) - 49 + 40= 0 \\ (x + 7)^(2) + (y - 5)^(2) - 9= 0 \\ (x + 7)^(2) + (y - 5)^(2) = 9 \\ (x + 7)^(2) + (y - 5)^(2) = {3}^(2) \\ equating \: it \: with \: \\ (x - h)^(2) + (y - k)^(2) = {r}^(2) \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3`