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
$(h - k)^2+(x + y)^2=r^2$.
$(x - h)^2+(y - k)^2=r^2$.
$(\frac{x}{h})^2+(\frac{y}{k})^2=r^2$.

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 \(d=\sqrt{(x - x_1)^2+(y - y_1)^2}\), where \(d = r\), \(x_1=h\), and \(y_1 = k\), squaring both sides gives \((x - h)^2+(y - k)^2=r^2\).

Answer:

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