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 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 equal to 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 the standard - form equation.

Answer:

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