What is the equation of the circle with the center (-1,-2) and passes through the point (6,4)?

  (x +1)^2 +(y +2)^2 = 85

Step-by-step explanation:

The equation of a circle with center (h, k) and passing through (a, b) is ...

  (x -h)^2 + (y -k)^2 = (a -h)^2 +(b -k)^2

Filling in your numbers gives ...

  (x -(-1))^2 +(y -(-2))^2 = (6 -(-1))^2 +(4 -(-2))^2 = 49 +36 = 85

  (x +1)^2 +(y +2)^2 = 85

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: