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

Explanation:

Step1: Recall circle - equation concept

The standard - form equation of a circle 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 \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \((x_1,y_1)=(h,k)\) and \((x_2,y_2)=(x,y)\) and \(d = r\), we square both sides to get \((x - h)^2+(y - k)^2=r^2\).

Answer:

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