Draw up the equation of a circle with the center of point A (5.6) and passing through point M, if M (-12.5)

The equation of a circle centered at point A (5; 6) and radius R is as follows.

(x – 5) ^ 2 + (y – 6) ^ 2 = R ^ 2.

Since the circle passes through the point M (- 12; 5), the coordinates of this point turn our equation into a true equality. We calculate R ^ 2.

Substitute x = – 12 and y = 5 into the equation.

(- 12 – 5) ^ 2 + (5 – 6) ^ 2 = R ^ 2,

(- 17) ^ 2 + (- 1) ^ 2 = R ^ 2,

289 + 1 = R ^ 2,

290 = R ^ 2.

This means that the equation of our circle will take the form (x – 5) ^ 2 + (y – 6) ^ 2 = 290.