Write the equation of a circle with center upper c left-parenthesis 4 comma negative 5 right-parenthesis that passes through upper p left-parenthesis 1 comma negative 2 right-parenthesis number .

The square of the distance between C(4, -5) and P(1, -2) is given by the Pythagorean theorem as
  (4-1)² +(-5-(-2))² = 18
This is the square of the radius of the circle, so we can use it for r² in the formula
  (x -h)² +(y -k)² = r² . . . . . . . circle of radius r and center (h, k)

Your circle has equation ...
  (x -4)² +(y +5)² = 18