Question

find the standard equation for the circle having the given center and radius. center (0,0) radius 9 the standard equation is (simplify your answer.)

Explanation:

Step1: Recall the standard circle equation

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

Here, the center is \((0,0)\), so \(h = 0\) and \(k = 0\), and the radius \(r = 9\). Substituting these into the formula, we get \((x - 0)^2+(y - 0)^2=9^2\).

Step3: Simplify the equation

Simplifying \((x - 0)^2+(y - 0)^2=9^2\) gives \(x^2 + y^2=81\).

Answer:

\(x^2 + y^2 = 81\)