Question

find the center of the circle.
3(x - 5)^2 + 3(y + 9)^2 = 48
center = (?, )

Explanation:

Step1: Simplify the equation

Divide both sides of the equation \(3(x - 5)^2+3(y + 9)^2 = 48\) by \(3\).
We get \((x - 5)^2+(y + 9)^2=16\).

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

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle.
For the equation \((x - 5)^2+(y+9)^2=(4)^2\) (since \(r^2 = 16\) implies \(r = 4\)), we can rewrite \(y+9\) as \(y-(-9)\).

Answer:

\((5,-9)\)