Question

which explains how to find the radius of a circle whose equation is in the form $x^{2}+y^{2}=z$?
the radius is the constant term, z.
the radius is the constant term, z, divided by 2.
the radius is the square root of the constant term, z.
the radius is the square of the constant term, z.

Explanation:

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

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

Step2: Analyze the given equation \(x^{2}+y^{2}=z\)

In the equation \(x^{2}+y^{2}=z\), we can rewrite it as \((x - 0)^2+(y - 0)^2=z\). Comparing with the standard form \((x - a)^2+(y - b)^2=r^2\), we have \(r^{2}=z\).

Step3: Solve for \(r\)

Taking the square root of both sides of the equation \(r^{2}=z\) (since radius \(r\geq0\)), we get \(r = \sqrt{z}\).

Answer:

The radius is the square root of the constant term, \(z\).