57. Write the equation of the circle in standard form with the given information .?

The equation of the circle in standard form with the given information:

Center : (1, - 4), Point on Circle : (- 9, - 2)

(x - 1)^2 + (y + 4)^2 = 104

1st solve for the radius.

(x -  h)^2 + (y - k)^2 = r^2

(- 9 -  1)^2 + (-2, - (-4))^2 = r^2

100 + 4 = r^2

r^2 = 104

Therefore, the equation of the circle is

(x - 1)^2 + (y + 4)^2 = 104.... Answer//

Hint: Expect (x - h)^2 + (y - k)^2 = r^2

Radius r is distance from centre  (h, k) = (1, - 4) to that point on Circle (- 9, - 2)

Change in x coordinate is 10

Change in y coordinate is 2

What is r^2 ?