Question

transform the polar equation to an equation in rectangular coordinates then identify and graph the equation. $r\cos\theta = 3$ what is the graph of this equation? a. vertical line b. circle with center at $(0, 3)$ c. horizontal line d. circle with center at $(3, 0)$ select the graph of $r\cos\theta = 3$.

Explanation:

Step1: Use the conversion formula

We know that in polar - rectangular conversion, \(x = r\cos\theta\).

Step2: Substitute the formula

Given \(r\cos\theta=3\), substituting \(x = r\cos\theta\) into the polar equation, we get \(x = 3\).

The equation \(x = 3\) represents a vertical line. A vertical line has the form \(x = k\) (where \(k\) is a constant), and for any value of \(y\), \(x\) is always \(3\).

Answer:

A. vertical line