Write down the equation of a circle centered at point C (3; -5), tangent to the ordinate.

As you know, the equation of the circle has the following form:

(x – x0) ² + (y – y0) ² = R²;

Values used:

x0 – 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 a point with coordinates C (3; -5), which means: x0 = 3, y0 = -5. It remains to determine the radius of the circle. Since it is known that it touches the ordinate axis, you need a distance from the point C (3; -5) to the Oy axis. This will be the module of the ordinate of point C: | -5 | = 5. Hence, R = 5.

Substituting the data into the formula, we get:

(x – 3) ² + (y – (-5)) ² = 5²;

(x – 3) ² + (y + 5) ² = 25.