Question

write the standard form of the equation of the circle with the given center and radius. center (4,7), r = 8. type the standard form of the equation of the circle. (simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

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

Given center $(4,7)$ and $r = 8$, so $h = 4$, $k = 7$, and $r=8$.

Step3: Substitute values into formula

Substitute $h = 4$, $k = 7$, and $r = 8$ into the formula: $(x - 4)^2+(y - 7)^2=8^2$.

Step4: Simplify the equation

$(x - 4)^2+(y - 7)^2=64$.

Answer:

$(x - 4)^2+(y - 7)^2=64$