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

Explanation:

Step1: Recall circle - standard - form formula

The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$.

Step2: Substitute given values

Given $h = 0$, $k = 1$, and $r = 1$. Substitute these values into the formula: $(x-0)^2+(y - 1)^2=1^2$.

Step3: Simplify the equation

$x^{2}+(y - 1)^{2}=1$.

Answer:

$x^{2}+(y - 1)^{2}=1$