Equation of a Circle Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Write the equation of the circle with center

(3, -2)

and radius

5

1
The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center and $r$ is the radius.
2
Substitute $h = 3$ , $k = -2$ , $r = 5$ .
3
$(x - 3)^2 + (y + 2)^2 = 25$ .

Answer

(x - 3)^2 + (y + 2)^2 = 25

The equation of a circle is derived from the distance formula: every point

(x, y)

on the circle is exactly

r

units from the center

(h, k)

. This gives

\sqrt{(x-h)^2 + (y-k)^2} = r

, which when squared yields the standard form.

About Equation of a Circle

The standard form equation $(x - h)^2 + (y - k)^2 = r^2$ describes a circle with center $(h, k)$ and radius $r$ in the coordinate plane.

Find the center and radius of the circle [formula].

Find the equation of the circle that has a diameter with endpoints [formula] and [formula].

Determine whether the circles [formula] and [formula] intersect, and find the number of intersection