Question

The polar equation $\cos \theta +7\sin \theta =\frac{1}{r}$ represents a

• A. circle
• B. parabola
• C. straight line
• D. hyperbola

Answer 1

Answer: (C)

straight line

$x=rcos\theta$ and $y=rsin\theta$ where $r=\sqrt{x^2+y^2}$.

Hence

$cos\theta +7sin\theta =\frac{1}{r}$

$\to \left(rcos\theta \right)+7\left(rsin\theta \right)=1$

$x+7y=1$

This represents a straight line.