Answer:
(x - 6)² + (y + 2)² = 242
Explanation:
Equation of a circle with center (a, b) and radius r is
(x - a)² + (y - b)² = r²
Given center is at (6, -2) the equation becomes
(x - 6)² + (y - (-2))² = r²
(x-6)² + (y+2)² = r²
Since the circle passes through point (-5, 9), these coordinates must satisfy the above equation.
Plugging in values we get
(-5 -6)² + (9+2)² = r²
Or,
r² = 11² + 11² = 121 + 121 = 242
So the equation of the circle is
(x - 6)² + (y + 2)² = 242