Question

Which statement describes how to derive the equation of a circle in standard​ form?

A. The equation of a circle can be derived using the quadratic formula.
B. The equation of a circle can be derived by solving a quadratic equation using the method of completing the square.
C. The equation of a circle can be derived using the midpoint formula.
D. The equation of a circle can be
derived using the distance formula.

Answer 1

The equation of a circle in standard form can be derived using the distance formula by setting the distance from the center to any point on the circle equal to the radius and then simplifying.

Step-by-step explanation:

The equation of a circle in standard form can be derived using the distance formula. The standard form of a circle's equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is its radius. To derive the equation, consider any point (x, y) on the circle. Using the distance formula, the distance from the center (h, k) to the point (x, y) must be equal to the radius r. By squaring both sides of the distance formula and arranging terms, we obtain the standard form of the equation of a circle.