Question

write the standard form of the equation of the circle with the given center and radius. center (2,6), r = 7 type the standard form of the equation of the circle. (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 $(2,6)$, so $h = 2$, $k = 6$, and $r = 7$.

Step3: Substitute values into the formula

Substitute $h = 2$, $k = 6$, and $r = 7$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 2)^2+(y - 6)^2=7^2$.

Step4: Simplify the equation

Since $7^2 = 49$, the equation of the circle is $(x - 2)^2+(y - 6)^2=49$.

Answer:

$(x - 2)^2+(y - 6)^2=49$