Question

fill in each blank so that the resulting statement is true. the standard form of the equation of a circle with center (h,k) and radius r is ________. the standard form of the equation of a circle with center (h,k) and radius r is

Explanation:

The standard form of a circle's equation is derived from the distance formula. The distance between any point \((x,y)\) on the circle and the center \((h,k)\) is the radius \(r\). Using the distance formula \(d = \sqrt{(x - h)^2+(y - k)^2}\), and since \(d=r\), squaring both sides gives \((x - h)^2+(y - k)^2=r^2\).

Answer:

\((x - h)^2+(y - k)^2=r^2\)