Question

write the standard form of the equation of the circle with the given center and radius.
center (6,2), r = 7

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

Given \(h = 6\), \(k = 2\), and \(r = 7\). Substitute these into the formula: \((x - 6)^2+(y - 2)^2=7^2\).

Step3: Simplify the right - hand side

Since \(7^2=49\), the equation becomes \((x - 6)^2+(y - 2)^2=49\).

Answer:

\((x - 6)^2+(y - 2)^2=49\)