Question

find the standard form of the equation for the circle with the following properties. radius $sqrt{11}$ and center $(7, - 3)$

Explanation:

Step1: Recall circle - equation formula

The standard - form 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 that the center is $(7,-3)$, so $h = 7$, $k=-3$, and the radius $r = \sqrt{11}$.

Step3: Substitute values into the formula

Substitute $h = 7$, $k=-3$, and $r=\sqrt{11}$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 7)^2+(y+3)^2=(\sqrt{11})^2$.

Step4: Simplify the equation

Since $(\sqrt{11})^2 = 11$, the standard - form equation of the circle is $(x - 7)^2+(y + 3)^2=11$.

Answer:

$(x - 7)^2+(y + 3)^2=11$