Question

write the standard form of the equation of the circle with the given center and radius. center (-1,-3), r = \sqrt{3}
the equation of the circle in standard form is . (simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify values of $h$, $k$, and $r$

Given center $(-1,-3)$, so $h=-1$, $k = - 3$, and $r=\sqrt{3}$.

Step3: Substitute values into the formula

Substitute $h=-1$, $k=-3$, and $r = \sqrt{3}$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-1))^2+(y - (-3))^2=(\sqrt{3})^2$.

Step4: Simplify the equation

$(x + 1)^2+(y + 3)^2=3$.

Answer:

$(x + 1)^2+(y + 3)^2=3$