Question

write the equation in standard form for the circle $x^{2}+y^{2}-1 = 0$.

Explanation:

Step1: Recall the standard form of a circle equation

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

Step2: Rearrange the given equation

Given \(x^{2}+y^{2}-1 = 0\), we can rewrite it as \(x^{2}+y^{2}=1\). Here, \(h = 0\), \(k = 0\) and \(r^{2}=1\) (so \(r = 1\)).

Answer:

\(x^{2}+y^{2}=1\)