Question

give the equation of the circle centered at the origin with radius 10.

Explanation:

Step1: Recall the standard equation of a circle

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

Step2: Substitute the values of center and radius

Since the center is at the origin \((0,0)\) (so \(h = 0,k = 0\)) and radius \(r = 10\), substitute these into the formula: \((x-0)^2+(y - 0)^2=10^2\).

Step3: Simplify the equation

\(x^2+y^2 = 100\).

Answer:

\(x^2+y^2=100\)