Question

A circle is represented by the equation x2+y2−16x−6y=−24 . Complete the square to discover the center and radius of the circle.(1 point)

center= (16,6) , radius=8

center= (8,3) , radius=7

center= (3,8) , radius=7

center= (−16,−6) , radius=8

Answer 1

Complete the square:

x^2 − 16x = (x − 8)^2 − 64
y^2 − 6y = (y − 3)^2 − 9

So
(x − 8)^2 − 64 + (y − 3)^2 − 9 = −24
(x − 8)^2 + (y − 3)^2 = 49

Thus center = (8, 3) and radius = 7.