Chapter 11.3, Problem 24E

To determine

To determine: The equivalent Cartesian equation for the given polar equation. Also, identify the graph without using a grapher.

Answer to Problem 24E

The required equation is $x^2+y^2=1$ and the equation is an equation of a circle whose radius is 1 and center is $\left(0,0\right)$ .

Explanation of Solution

Given information:

The polar equation: $r^2=1$

Calculation:

The given equation is $r^2=1$ .

To find the required Cartesian equation, use the formulas $x=r\cos \theta$ , $y=r\sin \theta$ , $r^2=x^2+y^2$ and $\tan \theta =\frac{y}{x}$ .

Substitute $x^2+y^2$ for $r^2$ in the given equation.

  $\begin{array}{c}{r}^2=1\\ x^2+y^2=1\end{array}$

The above equation is an equation of a circle whose radius is 1 and center is $\left(0,0\right)$ .

Hence, the required equation is $x^2+y^2=1$ and the equation is an equation of a circle whose radius is 1 and center is $\left(0,0\right)$ .