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 = 2; (h,k)=(0,2) the standard form of the equation of this circle is

Explanation:

Step1: Recall circle - standard form

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

Step2: Substitute given values

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

Step3: Simplify the equation

We get $x^{2}+(y - 2)^{2}=4$.

Answer:

$x^{2}+(y - 2)^{2}=4$