JEE Advance - Mathematics (1983 - No. 40)
The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$, $$y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point $$'\theta '$$ is such that
it makes a constant angle with the $$x$$-axis
it passes through the origin
it is at a constant distance from the origin
none of these