Question

The normal of the curve $x=d(cos\theta +\theta sin\theta )y=a(sin\theta -\theta cos\theta )$ at any $\theta$ is such that

[DCE 2000; AIEEE 2005]

• A. It makes a constant angle with x-axis
• B. It passes through the origin
• C. It is at a constant distance from the origin
• D. None of these

Answer 1

The correct option is C

It is at a constant distance from the origin

$y=a_0+a_{1}x+a_2{x}^2+a_n{x}^n$
$y_1=a_1+2a_{2}x+........+n{a}_n{x}^{n-1}$
$y_2=2a_2+6a_{3}x+........+n(n-1)a_n{x}^{n-2}$
............................................
............................................
$y_n=n!a_n.$