Find the center of a circle

Learning Objectives Identify the center of a circle directly from its standard equation. Calculate the center of a circle using the midpoint formula when given the endpoints of a diameter. Convert the general form of a circle's equation to the standard form by completing the square. Determine the center of a circle from its general form equation. Explain the geometric relationship between a circle's center, its diameter, and its radius. Recognize and avoid common errors, such as sign mistakes when identifying the center's coordinates. How does an earthquake seismograph pinpoint an epicenter? It finds the center of intersecting circles created by seismic waves! 🌍 This tutorial will teach you the essential skill of finding the center of a circle in the coordin...

TermDefinitionExample Center of a Circle (h, k)The single point inside a circle from which all points on the circle are an equal distance. It is represented by the coordinates (h, k).For a circle with its center at the origin, the coordinates are (0, 0). Radius (r)The fixed distance from the center of the circle to any point on the circle itself.If the center is at (2, 3) and a point on the circle is (2, 8), the radius is 5 units. DiameterA straight line segment that passes through the center of a circle and whose endpoints lie on the circle. Its length is twice the radius.If a circle's radius is 4, its diameter is 8. Standard Equation of a CircleThe equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.The equation (x - 1)^2 + (y + 4)^2 = 25 represents...

Standard Equation of a Circle (x - h)^2 + (y - k)^2 = r^2 Use this formula to directly identify the center of the circle, (h, k). Be careful with the signs: the coordinate is the opposite of the sign in the parentheses. Midpoint Formula M = ( (x_1 + x_2) / 2 , (y_1 + y_2) / 2 ) Use this formula to find the center of a circle when you are given the coordinates of the two endpoints of a diameter, (x_1, y_1) and (x_2, y_2).