What is the equation of the circle that has center (0,-8) and passes through (9,7)?

x² + y² + 16y - 242 = 0

Step-by-step explanation: The equation of circle is given in the form (x -a)² + (y - b)² = r², where (a,b) is the center of the circle and r is the radius. But r is the distance from (0,-8) to (9,7)

the equation is (x-0)² + (y + 8)² = r²

                           x² + (y + 8)² = r²

hence r² = (x₁ - x₂)² + (y₁ - y₂)²

          r² = (0 - 9)² + (-8 - 7)² = 81 + 225 = 306

hence the equation is

                x² + y²+16y+64 = 306

                x² + y² + 16y - 242 = 0