Question

write the standard form of the equation of the circle with the given center and radius.
center (5,6), r = 8

type the standard form of the equation of the circle.
(simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Substitute the given values into the formula

Given \(h = 5\), \(k = 6\), and \(r = 8\). Substitute these into \((x - h)^2+(y - k)^2=r^2\) to get \((x - 5)^2+(y - 6)^2=8^2\).

Step3: Simplify the equation

Since \(8^2=64\), the equation becomes \((x - 5)^2+(y - 6)^2=64\).

Answer:

\((x - 5)^2+(y - 6)^2=64\)