Question

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

Explanation:

Step1: 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 and \(r\) is the radius.

Step2: Identify the center

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

Step3: Identify the radius

We know that \(r^2 = 324\). Taking the square - root of both sides, \(r=\sqrt{324}\). Since \(18\times18 = 324\), \(r = 18\).

Answer:

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