Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle. r = 1; (h,k)=(0,1) the standard form of the equation of this circle is $x^{2}+(y - 1)^{2}=1$. the general form of the equation of this circle is (simplify your answer.)

Explanation:

Step1: Expand the standard - form equation

\[

$$\begin{align*} x^{2}+(y - 1)^{2}&=1\\ x^{2}+y^{2}-2y + 1&=1 \end{align*}$$

\]

Step2: Simplify to get the general form

\[
x^{2}+y^{2}-2y=0
\]

Answer:

\(x^{2}+y^{2}-2y = 0\)