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= (3,8)
, radius=7

center= (16,6)
, radius=8

center= (−16,−6)
, radius=8

center= (8,3)
, radius=7

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.