Find the radius or diameter of a circle

Learning Objectives Find the radius and diameter of a circle given its equation in standard form. Find the radius and diameter of a circle by converting its equation from general form to standard form using the method of completing the square. Calculate the radius of a circle using the distance formula when given the coordinates of the center and one point on the circumference. Determine the radius of a circle by first finding the center and then the length of the radius when given the endpoints of a diameter. Analyze the value of r^2 to determine if an equation represents a circle, a point (a degenerate circle), or is an impossible case. Solve applied problems involving the radius or diameter of a circle. Ever wondered how GPS pinpoints your location using intersecting circ...

TermDefinitionExample Radius (r)The distance from the center of a circle to any point on its circumference.In a circle with center (0,0) and a point (4,0) on its edge, the radius is 4 units. Diameter (d)The distance across a circle passing through its center. It is always twice the length of the radius (d = 2r).If a circle's radius is 7 units, its diameter is 14 units. Center (h, k)The fixed point from which all points on the circle are equidistant.In the equation (x - 2)^2 + (y + 5)^2 = 9, the center is (2, -5). Standard Equation of a CircleThe form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.(x - 1)^2 + (y - 3)^2 = 16 represents a circle with center (1, 3) and radius 4. General Equation of a CircleThe form x^2 + y^2 + Dx + Ey + F = 0, which can be co...

Radius from Standard Form (x - h)^2 + (y - k)^2 = r^2 In the standard equation of a circle, the radius 'r' is the principal square root of the constant term on the right side of the equation. Always remember that the equation gives you r², not r. Finding Radius from General Form If x^2 + y^2 + Dx + Ey + F = 0, then r^2 = (D/2)^2 + (E/2)^2 - F To find the radius from the general form, you must first convert it to standard form by completing the square for both x and y terms. The resulting constant on the right side of the equation is r². The radius is then r = √((D/2)² + (E/2)² - F), provided the result is positive. Radius using the Distance Formula r = \sqrt{(x_{point} - h)^2 + (y_{point} - k)^2} When you know the center of the circle (h, k) and any point o...