Chapter 11: Parametric Equations and Polar Coordinates - Section 11.3 - Polar Coordinates - Exercises 11.3 - Page 663: 48

The graph is a circle with center: $(\dfrac{3}{2},0)$ having radius $\dfrac{3}{2}$.

Work Step by Step

The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$ 2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ 3. $x=r \cos \theta$ and 4. $y=r \sin \theta$ Given: $r^2=3r \cos \theta$ Thus, the Cartesian equation is $x^2+y^2=3x$ or, $(x-\dfrac{3}{2})^2+y^2=\dfrac{9}{4}$ Hence, this shows that the graph is a circle with center: $(\dfrac{3}{2},0)$ having radius $\dfrac{3}{2}$.

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