Verified answer

r = 12 cos θ

√(x^2 + y^2) = 12 x/√(x^2 + y^2)

x^2 + y^2 = 12x

This is a circle, with radius 6, centered at (6, 0) on the x-axis or principal axis.

Use following substitutions when transforming between polar and rectangular:

x = r cos(t)

y = r sin(t)

x² + y² = r²

r = 12 cos(t) . . . . . . . multiply both sides by r

r² = 12 r cos(t) . . . . . use substitutions

x² + y² = 12x

This is equation of circle. Complete the square to find centre and radius:

x² - 12x + y² = 0

x² - 12x + 36 + y² = 36

(x - 6)² + y² = 36

Circle with centre (6,0) and radius = 6