Find a cartesian equation for the curve and identify it. r = 7 cos(θ)

Solution:

Given r = 7 cos θ

Multiplying throughout by ‘r’,

r² = 7r cos θ --- (1)

Consider x² + y² = r² and put x = r cos θ --- (2)

x² + y² = 7x

Using completing square method,

x² - 7x + (7/2)² + y² = (7/2)²

[x - (7/2)]² + y² = 49/4

(x - 7/2)² + (y - 0)² = (7/2)²

This is the equation of circle with center (7/2, 0) and radius 7/2.

Find a cartesian equation for the curve and identify it. r = 7 cos(θ)

Summary:

The cartesian equation for the curve r = 7 cos(θ) is [x - (7/2)]² + y² = 49/4, which is the equation of a circle.