Question

Polar to Rectangular Sketch a graph of the polar equation, and express the equation in rectangular coordinates.

$r=2$.

Short answer

The equation in rectangular coordinates is$x^2+y^2=4$ .

Step-by-step solution

Step 1. Given information.

The given polar equation is$r=2$ .

Step 2.  To express the polar equation in rectangular coordinates.

Squaring both sides of the equation to get an equivalent equation in rectangular coordinates.

The graph consists of all points whose r-coordinate is 2, that is, all points that are 2 units away from the origin. So the graph is a circle of radius 2 centered at the origin. Squaring both sides of the equation$r=2$,

$\begin{array}{c}{r}^2=2^2\\ x^2+y^2=4\end{array}$

Substituting,$r^2=x^2+y^2$

So the equivalent equation in rectangular coordinates is $x^2+y^2=4$.