Question

write the equation in standard form for the circle $x^{2}+y^{2}-16 = 0$.

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: Rewrite the given equation

Given \(x^{2}+y^{2}-16 = 0\), we can rewrite it as \(x^{2}+y^{2}=16\). Here \(h = 0\), \(k = 0\) (since there are no \(x\) or \(y\) - linear terms), and \(r^{2}=16\) (so \(r = 4\)).

Answer:

\(x^{2}+y^{2}=16\)