question_answer

The normal to the curve \[x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )\]at any point\['\theta '\]is such that     AIEEE  Solved  Paper-2005

A) it is at a constant distance from the origin

B) it passes through\[(a\text{ }\pi /2,-a)\]

C) it makes angle\[\pi /2+\theta \]with the X-axis

D) it passes through the origin

Correct Answer: A , C

Solution :

Equation of normal at any pointon any curve is Given that, On differentiating w.r.t.of respectively, we get                                            ...(i) and                                                 ..(ii) On dividing Eq. (ii) by Eq. (i), we get Slope of normal So, equation of normal is It is always at a constant distance 'a' from origin.

Solution :

Equation of normal at any pointon any curve is Given that, On differentiating w.r.t.of respectively, we get                                            ...(i) and                                                 ..(ii) On dividing Eq. (ii) by Eq. (i), we get Slope of normal So, equation of normal is It is always at a constant distance 'a' from origin.