Answer
$${\text{The equation represents a circle with radius }}r = \frac{3}{2}{\text{, centered at }}\left( {\frac{3}{2},0} \right)$$
Work Step by Step
$$\eqalign{
& r = 3\cos \theta \cr
& {\text{Multiply both sides of the equation by }}r \cr
& {r^2} = 3r\cos \theta \cr
& {\text{Convert to rectangular form, using }}x = r\cos \theta ,{\text{ }}{r^2} = {x^2} + {y^2} \cr
& {x^2} + {y^2} = 3\left( x \right) \cr
& {x^2} + {y^2} = 3x \cr
& {x^2} - 3x + {y^2} = 0 \cr
& {\text{Completing the square}} \cr
& {x^2} - 3x + \frac{9}{4} + {y^2} = \frac{9}{4} \cr
& {\left( {x - \frac{3}{2}} \right)^2} + {y^2} = {\left( {\frac{3}{2}} \right)^2} \cr
& {\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr
& {\text{The equation represents a circle with radius }}r = \frac{3}{2} \cr
& {\text{Centered at }}\left( {\frac{3}{2},0} \right) \cr
& {\text{Graph}} \cr} $$
