Question

The equation $\frac{5}{r}=4+3\cos \theta$ represents :
(Note : $r$ and $\theta$ are the polar coordinates)

• A. a parabola
• B. an ellipse
• C. a hyperbola
• D. a rectangular hyperbola

Answer 1

The correct option is B an ellipse

Given, the polar equation $\frac{5}{r}=4+3\cos \theta$
$\Rightarrow r=\frac{5}{4+3\cos \theta }$
$\Rightarrow r=\frac{\frac{5}{4}}{1+\frac{3}{4}\cos \theta }$
Here, $e=\frac{3}{4}<1$
Hence, the given equation represents an ellipse.