Question

find the standard form of the equation of the circle with center (6, - 5) and circumference 18π. the equation is . (simplify your answer. type an exact answer, using π as needed.)

Explanation:

Step1: Find the radius

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=18\pi$, we set up the equation $18\pi=2\pi r$. Solving for $r$ by dividing both sides by $2\pi$, we get $r = 9$.

Step2: Write the standard - form equation

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. Here, $h = 6$, $k=-5$ and $r = 9$. Substituting these values into the formula, we have $(x - 6)^2+(y+5)^2=81$.

Answer:

$(x - 6)^2+(y + 5)^2=81$