Question

determine the center and radius of the circle.
$(x - 4)^{2}+(y - 5)^{2}=81$
part 1 of 2
the center is $(4,5)$.
part: 1 / 2
part 2 of 2
the radius is $r =$

Explanation:

Step1: Recall the standard form of a circle 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 radius

Given \((x - 4)^2+(y - 5)^2=81\), we can rewrite \(81\) as \(9^2\) (since \(r^2 = 81\)). So, \(r=\sqrt{81}\).

Answer:

\(r = 9\)