Question

write the standard form of the equation of the circle with the given center and radius. center (5,3), r = 6 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 \(h = 5\), \(k = 3\), and \(r = 6\). Substitute these into \((x - h)^2+(y - k)^2=r^2\) to get \((x - 5)^2+(y - 3)^2=6^2\).

Step3: Simplify the equation

Since \(6^2=36\), the equation becomes \((x - 5)^2+(y - 3)^2=36\).

Answer:

\((x - 5)^2+(y - 3)^2=36\)