Question

write the standard form of the equation of the circle of radius r = 8 and center (h,k)=(0,0). graph the circle. the standard form of the equation of this circle is . use the graphing tool to graph a circle with center (0,0) and a radius of 8. click to enlarge graph

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute given values

Given \(h = 0\), \(k = 0\), and \(r = 8\). Substitute these values into the formula: \((x-0)^2+(y - 0)^2=8^2\).

Step3: Simplify the equation

\(x^{2}+y^{2}=64\).

Answer:

\(x^{2}+y^{2}=64\)