Equations of Circles

The standard form of the equation of a circle is: $$(x-h)^2 + (y-k)^2 = r^2$$ , where (h, k) is the center and r is the radius.

To find the radius from the equation $$(x-h)^2 + (y-k)^2 = r^2$$ , take the square root of r^2. For example, if r^2 = 16, then the radius r = 4.

The center of a circle in the equation $$(x-h)^2 + (y-k)^2 = r^2$$ is the point (h, k) around which the circle is drawn.

The standard form is $$(x+2)^2 + (y+3)^2 = 49$$ .

The radius is 4 units, since r^2 = 16.

The equation is $$(x-4)^2 + (y+2)^2 = 9$$ .

To complete the square, rearrange the equation to group x and y terms, then add the necessary constants to both sides to form perfect squares.

The general form is $$x^2 + y^2 + Dx + Ey + F = 0$$ , where D, E, and F are constants.

The center is (-1, 5) and the radius is 5 units.

The radius is the distance from the center of the circle to any point on its circumference.