Question

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

• A. $x \cos \theta - y \sin \theta = a \cos 2 \theta$
• B. $x \cos \theta + y \sin \theta = a \cos 2 \theta$
• C. $x \sin \theta + y \cos \theta = a \cos 2 \theta$
• D. None of these

Answer 1

Answer: (A)

$x \cos \theta - y \sin \theta = a \cos 2 \theta$

Answer 2

$x \cos \theta - y \sin \theta = a \left( \cos ^ { 4 } \theta - \sin ^ { 4 } \theta \right) = a \cos 2 \theta$ .