Question

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

Explanation:

Step1: Simplify the equation by dividing both sides by 6

$$\begin{align*} \frac{6(x - 3)^2+6(y + 7)^2}{6}&=\frac{216}{6}\\ (x - 3)^2+(y + 7)^2&=36 \end{align*}$$

Step2: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - a)^2+(y - b)^2=r^2\), where \(r\) 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 \(r\)

Take the square root of both sides: \(r=\sqrt{36}\)

Answer:

\(6\)