Write the equation of a circle with center C (2; 2) and passing through D (5; 5).

The coordinates of the center of the circle are known. To write her equation, we do not have enough radius value.

The coordinates of the point that belongs to the circle are also known. We can find the radius as the distance between the center of the circle and a given point – we get the radius of the circle from its definition. For convenience, we will immediately find the square of the segment size:

| OD | ^ 2 = (5 – 2) ^ 2 + (5 – 2) ^ 2 = 18;

We get the equation of the circle:

(x – 2) ^ 2 + (y – 2) ^ 2 = 18.