Standard Form for the Equation of the Circle A circle is a set of points in a plane that are a given distance from a fixed point in the plane. The fixed point is called the center of the circle and the given distance is called the radius. The standard form of the circle with center (h, k) and radius r is (x, y) r (h, k)

More about the Equation of the Circle Problem. Write the equation of the circle with center at (2, 5) and radius 3. Use h =2, k=5, and r=3 in the standard form. Problem. Find the center and radius of the circle whose equation is Solution. Let h = 1, k = 3, r = 2 in the standard form. So the center is (1, 3) and the radius is 2. Problem. Write the equation of the circle with center at C(1, 2) which passes through the point P(3,4). Solution. So the equation is

General Form of the Equation of a Circle Suppose we are given an equation of the form Then we may rewrite the equation in standard form by completing the square in each variable. Example. Write the following equation in standard form.

Summary of The Circle; We discussed Standard form for the equation of a circle General form for the equation of a circle Conversion from the general form to the standard form