Straight Line Question 111

Question: The length of perpendicular from the point $ (a\cos \alpha ,a\sin \alpha ) $ upon the straight line $ y=x\tan \alpha +c, $ $ c>0 $ is [MP PET 2004]

Options:

A) $ c\cos \alpha $

B) $ c{{\sin }^{2}}\alpha $

C) $ c{{\sec }^{2}}\alpha $

D) $ c{{\cos }^{2}}\alpha $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Here, equation of line is $ y=x\tan \alpha +c $ , $ c>0 $ Length of the perpendicular drawn on line from point $ (a\cos \alpha ,a\sin \alpha ) $ $ p=\frac{-a\sin \alpha +a\cos \alpha \tan \alpha +c}{\sqrt{1+{{\tan }^{2}}\alpha }} $ ; $ p=\frac{c}{\sec \alpha }=c\cos \alpha $ .