Write down the equation of a circle centered at a (4; -7) and a radius of 6 cm

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

(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 (4; -7), that is: x0 = 4, y0 = -7. The radius of the circle, R = 6 cm.

Substituting these tasks into the main formula, we get:

(x – 4) ² + (y – (-7)) ² = 6²;

Let’s simplify the notation:

(x – 4) ² + (y + 7) ² = 36.

We got the desired equation for a given circle.