Find the radius of a circle

Learning Objectives Find the radius of a circle given its center and a point on the circle. Determine the radius of a circle from its equation in standard form, (x - h)² + (y - k)² = r². Find the radius 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 given the two endpoints of a diameter. Apply the Distance Formula as a primary tool for finding the radius. Explain the relationship between the radius, center, and the equation of a circle. How does your phone's GPS know your exact location using signals from satellites orbiting high above? 🛰️ It all comes down to circles and their radii! In this tutorial, you will master several methods for finding the radius, a critical...

TermDefinitionExample CircleThe set of all points in a plane that are at a fixed distance from a fixed point. The fixed point is the center, and the fixed distance is the radius.All points that are exactly 5 units away from the point (2, 3). Center (h, k)The fixed point from which all points on the circle are equidistant.In the equation (x - 4)² + (y + 1)² = 25, the center is (4, -1). Radius (r)The distance from the center of the circle to any point on the circle. It is always a positive value.If a circle has its center at (0, 0) and the point (3, 4) is on the circle, the radius is 5 units. DiameterA line segment that passes through the center of the circle and has its endpoints on the circle. Its length is twice the radius (d = 2r).If a circle's radius is 6, its diameter is 12. Stan...

The Distance Formula r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this to find the radius (r) when you know the coordinates of the center (x₁, y₁) and any point on the circle (x₂, y₂). The radius is simply the distance between these two points. The Standard Equation of a Circle (x - h)^2 + (y - k)^2 = r^2 Use this to find the radius when the circle's equation is given in standard form. The radius 'r' is the square root of the constant term on the right side of the equation. The Midpoint Formula Center (h, k) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) This isn't for the radius directly, but it's a crucial first step. Use it to find the center of the circle if you are given the endpoints of a diameter, (x₁, y₁) and (x₂, y₂). Once you have the...