Equate a circle centered on the x-axis through points (-4; 4) and (-2; 0).

Since the center of the circle lies on the X axis, it will have coordinates (x0; 0).

The coordinates of two points belonging to the circle are known.

The distance from these points to the center of the circle is equal, based on the concept of the radius of the circle.

Let’s write formulas for finding the distance between points, after which we equate the expressions:

| OM | ^ 2 = (x0 + 4) ^ 2 + 16;

| ON | ^ 2 = (x0 + 2) ^ 2;

We equate the squares of the segments for convenience:

(x0 + 4) ^ 2 + 16 = (x0 + 2) ^ 2;

x0 ^ 2 + 8 * x0 + 16 + 16 = x0 ^ 2 + 4 * x0 + 4;

4 * x0 = -28;

x0 = -7.

We have the center of the circle (-7; 0). Then:

R = | ON | = ((-7 + 2) ^ 2) ^ (1/2) = 5;

(x + 7) ^ 2 + y ^ 2 = 25 is the equation of the circle.