Question

write the standard form of the equation of the circle with the given center and radius. center (7,4), r = 3 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

Here, \(h = 7\), \(k = 4\), and \(r = 3\). Substituting these values into the formula gives \((x - 7)^2+(y - 4)^2=3^2\).

Step3: Simplify the right - hand side

Since \(3^2=9\), the equation becomes \((x - 7)^2+(y - 4)^2=9\).

Answer:

\((x - 7)^2+(y - 4)^2=9\)