equation 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.

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

The radius can be found by taking the square root of the right side of the equation in standard form: $$r = \text{sqrt}(r^2)$$ .

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

The equation is $$x^2 + y^2 = 25$$ .

The center is (-1, 2).

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

The general form is $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ , where A is not equal to 0.

The equation is $$(x - 3)^2 + (y + 4)^2 = 4$$ .

Completing the square is a method used to rewrite a quadratic equation in standard form by transforming it into a perfect square trinomial.