Question

The equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8}\cos \theta$ represents

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

Answer 1

The correct option is D a hyperbola

$\frac{1}{r}=\frac{1}{8}+\frac{3}{8}cos\theta$
$\Rightarrow \frac{8}{r}=1+3\cos \theta$
comparing with $\frac{l}{r}=1+e\cos \theta$
Hence eccentricity of conic is $e=3>1$
$\therefore$ The given conic is hyperbola.