Question

Graphs of Polar Equations Match the polar equation with the graphs labeled I-VI. Use the table on page 519 to help you.

.$r=3$

Short answer

The graph of the curve in its polar form with$r=3$ is the 3^rd graph

Step-by-step solution

Step 1.Given information.

A polar equation$r=3$

Step 2. We have to match the curve in the polar form with its graph.

We use the properties of polar coordinates to decipher the graph of the curve.

We have a curve in its polar form with r=3

To convert the points of a curve from polar coordinates to rectangular coordinates we use the formula$(r,\theta )=(\sqrt{x^2+y^2},{\tan }^{-1}\left(\frac{y}{x}\right))$Where (x,y) are the coordinates of that point on the coordinate system. So,

$\begin{array}{l}\Rightarrow \sqrt{x^2+y^2}=3\\ \Rightarrow x^2+y^2=3^2\end{array}$

This is the equation of a circle centered around the origin with radius as 3 units.
This curve has a graph as

So this curve has a graph that matches with the 3rd graph.