Question

write the standard form of the equation of the circle with the given center and radius. center (1,3), r = √7. the equation of the circle in standard form is . (simplify your answer.)

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 $(1,3)$, so $h = 1$, $k = 3$, and $r=\sqrt{7}$.

Step3: Substitute values into the formula

Substitute $h = 1$, $k = 3$, and $r=\sqrt{7}$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 1)^2+(y - 3)^2=(\sqrt{7})^2$.

Step4: Simplify the right - hand side

Since $(\sqrt{7})^2 = 7$, the equation of the circle in standard form is $(x - 1)^2+(y - 3)^2=7$.

Answer:

$(x - 1)^2+(y - 3)^2=7$