ISI2015-MMA-49

Question

The polar equation $r=a \cos \theta$ represents

• A. a spiral
• B. a parabola
• C. a circle
• D. none of the above

Answer 1

$\underline{\mathbf {Answer: C}}$

a circle.

$\underline{\mathbf{Explanation:}}$

Multiply both sides by $\mathbf r$ to get

$\mathrm{r^2 = ar\cos \theta}$

Now, on using the substitution $\color{blue} {\mathrm{r^2 = x^2 + y^2}}$ and $\color {blue} {\mathrm {r \cos \theta = x}}$ to get $\mathrm{x^2 + y^2 = ax}$ 

Then we get:

$\mathrm {{\left (x-\frac{a}{2}\right )}^2 + y^2 = \frac{a^2}{4}}$

$\therefore $ It forms a circle.