Which of the following is the standard form equation of a circle with center (h, k) and radius r?

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Multiple Choice

Which of the following is the standard form equation of a circle with center (h, k) and radius r?

All points on a circle are a fixed distance from the center. For a circle with center (h, k) and radius r, that distance to a generic point (x, y) must equal r. Using the distance formula and then squaring to remove the square root gives the equation (x − h)^2 + (y − k)^2 = r^2. The minus signs show the shift to place the center at (h, k); using plus signs would place the center at (−h, −k). The radius must be squared on the right side to match the squared distance, hence r^2. If the center were at the origin, h and k would be 0 and the equation would simplify to x^2 + y^2 = r^2.

All points on a circle are a fixed distance from the center. For a circle with center (h, k) and radius r, that distance to a generic point (x, y) must equal r. Using the distance formula and then squaring to remove the square root gives the equation (x − h)^2 + (y − k)^2 = r^2. The minus signs show the shift to place the center at (h, k); using plus signs would place the center at (−h, −k). The radius must be squared on the right side to match the squared distance, hence r^2. If the center were at the origin, h and k would be 0 and the equation would simplify to x^2 + y^2 = r^2.

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