Question

write the standard form of the equation of the circle with the given center and radius. center (0,0), r = 2. the equation for the circle in standard form is . (simplify your answer.)

Explanation:

Step1: Recall circle - standard form

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

Here, $h = 0$, $k = 0$, and $r = 2$. Substituting these into the formula, we get $(x-0)^2+(y - 0)^2=2^2$.

Step3: Simplify the equation

$(x-0)^2=x^2$, $(y - 0)^2=y^2$, and $2^2 = 4$. So the equation is $x^{2}+y^{2}=4$.

Answer:

$x^{2}+y^{2}=4$