General formula to make an equation of circle
(x - a)² + (y - b)² = r²
with a center at (a,b) and a point on the circle at (x,y), and r is the radius
First, find the radius of the circle
plug the numbers into the equation
(x - a)² + (y - b)² = r²
(-2 - 7)² + (-5 - 2)² = r²
(-9)² + (-7)² = r²
r² = 81 + 49
r² = 130
r = √130
Second, determine the equation
(x - a)² + (y - b)² = r²
(x - 7)² + (y - 2)² = 130
This is the equation.
If you need to simplify it, see the following steps
(x - 7)² + (y - 2)² = 130
x² - 14x + 49 + y² - 4y + 4 = 130
x² + y² - 14x - 4y + 49 + 4 - 130 = 0
x² + y² -14x - 4y - 77 = 0