## Problem

Find the standard form of the rectangular equation of the circle with polar equation

\[r = 4cos\theta \]

## Solution

We have the following relationships between polar coordinates and rectangular coordinates:

\[x = r cos\theta \]

\[u = r sin\theta \]

\[r^2 = x^2 + y^2 \]

Multiply both sides by r, we get

\[r^2 = 4rcos\theta \]

\[x^2 + y^2 = 4x \]

\[x^2 - 4x + y^2 = 0 \]

\[(x^2 - 4x + 4)+ y^2 = 4 \]

\[(x - 2)^2 + y^2 = 4 \]