Straight Line Question 326

Question: The equation to the straight line passing through the point $ (a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta ) $ and perpendicular to the line $ x\sec \theta +ycosec\theta =a, $ is [AMU 1975]

Options:

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

Show Answer

Answer:

Correct Answer: A

Solution:

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