Equations of a Circle

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 in standard form $$(x-h)^2 + (y-k)^2 = r^2$$ , take the square root of r^2.

The center of a circle is represented by the point (h, k) in the standard form equation $$(x-h)^2 + (y-k)^2 = r^2$$ .

The radius is 5, since $$r^2 = 25$$ and $$r = \sqrt{25} = 5$$ .

The radius is 4, since $$r^2 = 16$$ and $$r = \sqrt{16} = 4$$ .

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for x and y.

The center is (-5, 1).

The equation is $$x^2 + y^2 = 100$$ .

The value on the right side, r^2, represents the square of the radius of the circle.

The radius is 5, since $$r^2 = 25$$ .