Question

find the radius of the circle.
6(x - 3)^2 + 6(y + 7)^2 = 216
radius = ?

Explanation:

Step1: Simplify the given equation

Divide both sides of the equation $6(x - 3)^2+6(y + 7)^2 = 216$ by 6. We get $(x - 3)^2+(y + 7)^2=\frac{216}{6}=36$.

Step2: Recall the standard - form of a circle equation

The standard - form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.
Comparing $(x - 3)^2+(y + 7)^2 = 36$ with $(x - a)^2+(y - b)^2=r^2$, we have $r^2 = 36$.

Step3: Solve for the radius

Take the square root of both sides of the equation $r^2 = 36$. Since $r>0$ (radius is a non - negative quantity), $r=\sqrt{36}=6$.

Answer:

6