# Write down the equation of a circle centered at point A and radius AB A (0; -3) B (-1; 0) C (5; 2).

First, we find the radius of the circle using the formula for the distance between two points:

d = √ ((x2 – x1) ² + (y2 – y1) ²);

In this formula, the first point has coordinates (x1; y1) – A (0; -3), the second – (x2; y2) – B (-1; 0).

We get: AB = √ ((- 1 – 0) ² + (0 – (-3)) ²) = √ (1 + 9) = √10.

Thus, the radius of the circle is determined, R = √10.

Now we use the equation of the circle:

(x – x0) ² + (y – y0) ² = R²;

Where: x0 is the abscissa of the center of the circle; y0 is the ordinate of the center of the circle; R is the size of the radius of the circle.

By condition, the center of the circle is at point A (0; -3), x0 = 0, y0 = -3. Previously found R = √10.

Substituting the data into the formula, we get:

(x – 0) ² + (y – (-3)) ² = (√10) ²;

x² + (y + 3) ² = 10 is the desired equation of the circle.