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 standard circle equation

The standard form of a circle centered at the origin is $x^2 + y^2 = r^2$, where $r$ is the radius.

Step2: Compare with given equation

The given equation is $x^2 + y^2 = z$. Set equal to standard form: $r^2 = z$.

Step3: Solve for radius $r$

Take square root of both sides: $r = \sqrt{z}$.

Answer:

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