Question

question
find the center and radius of the circle represented by the equation below.
$$ ( x - 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 324 $$
answer attempt 1 out of 2
center: $$ ( square, square ) $$
radius: $$ square $$

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify the center

For the equation \((x - 2)^2+(y + 8)^2=324\), comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 2\) and \(k=-8\) (since \(y+8=y-(-8)\)).

Step3: Identify the radius

We know that \(r^2 = 324\). Taking the square root of both sides, \(r=\sqrt{324}=18\).

Answer:

Center: \((2,-8)\)
Radius: \(18\)