Question

write the standard form of the equation of the circle with the given center and radius. center (5,4), 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 \(h = 5\), \(k = 4\), and \(r = 8\). Substitute these into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 5)^2+(y - 4)^2=8^2\).

Step3: Simplify the right - hand side

Since \(8^2=64\), the equation becomes \((x - 5)^2+(y - 4)^2=64\).

Answer:

\((x - 5)^2+(y - 4)^2=64\)