Question

write the standard form of the equation of the circle with the given center and radius. center (5,4), r = 7 type the standard form of the equation of the circle. (simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute the given values

Given \(h = 5\), \(k = 4\), and \(r = 7\). Substitute these values into the formula: \((x - 5)^2+(y - 4)^2=7^2\).

Step3: Simplify the right - hand side

\(7^2=49\), so the equation is \((x - 5)^2+(y - 4)^2 = 49\).

Answer:

\((x - 5)^2+(y - 4)^2 = 49\)