Question

transform the polar equation to an equation in rectangular coordinates. then identify and graph the equation
$r\cos\theta = 3$
what is the standard form of the equation in rectangular form?
$x = 3$
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 $(3,0)$

Explanation:

Step1: Recall the relationship between polar and rectangular coordinates

In polar coordinates, \(x = r\cos\theta\).

Step2: Substitute the relationship into the given polar equation

Given \(r\cos\theta = 3\), substituting \(x=r\cos\theta\) gives \(x = 3\).

Step3: Analyze the graph of \(x = 3\)

The equation \(x=3\) represents a vertical line where for all values of \(y\), \(x\) is always \(3\).

Answer:

A. vertical line