Question

The equation of straight line which passes through the point ($a \cos ^{3} \theta, a \sin ^{3} \theta)$ and perpendicular to $x \sec \theta+y \operatorname{cosec} \theta=a$ is

• A. $\frac{x}{a}+\frac{y}{a}=a \cos \theta$
• B. $x \cos \theta-y \sin \theta=a \cos 2 \theta$
• C. $x \cos \theta+y \sin \theta=a \cos 2 \theta$
• D. $x \cos \theta-y \sin \theta=-a \cos 2 \theta$

Answer 1

Answer: (B)

$\frac{ x }{\sin \theta}-\frac{ y }{\cos \theta}=\frac{ a \cos ^{3} \theta}{\sin \theta}-\frac{ a \sin ^{3} \theta}{\cos \theta}$
$\frac{ x \cos \theta- y \sin \theta}{\sin \theta \cos \theta}=\frac{ a (\cos 2 \theta)}{\sin \theta \cos \theta}$
$x \cos \theta- y \sin \theta= a \cos 2 \theta$