Find an equation of the circle that has center (6, 2) and passes through (-2,-6).

(x - 6)² + (y - 2)² = 128

Step-by-step explanation:

Given as the circle has center ( 6 , 2)

and it passes through points (-2 , -6)

Now , standard equation of circle is (x -a)² + (y- b)² = r²   , where (a , b) is center and r is the radius .

Again from given center the circle equation is

(x- 6)² + (y- 2)² = r²

Now this circle passes through points (-2 , -6)

so, (-2 -6)² + (-6 -2)²  = r²

so, 8²  + 8² = r²

Or, 128  = r²

i.e Radius pf this circle = 8

Hence the circle equation formed is

(x- 6)² +( y-2)² = 128   Answer