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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.