Question

write an equation of a circle centered at the origin with a radius of 8 in standard form. the equation of the circle in standard form is

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Substitute the values of center and radius

Since the center is at the origin \((0,0)\) (so \(h = 0,k = 0\)) and \(r = 8\), we substitute these into the formula: \((x - 0)^2+(y - 0)^2=8^2\).

Step3: Simplify the equation

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

Answer:

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