Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle. r = 10; (h,k)=(-6,8) the standard form of the equation of this circle is

Explanation:

Step1: Recall the standard - form 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: Substitute the given values

Given $h=-6$, $k = 8$, and $r = 10$. Substitute these values into the formula:
$(x-(-6))^2+(y - 8)^2=10^2$.

Step3: Simplify the equation

$(x + 6)^2+(y - 8)^2=100$.

Answer:

$(x + 6)^2+(y - 8)^2=100$