JEE Advance - Mathematics (1991 - No. 17)
Three normals are drawn from the point $$(c, 0)$$ to the curve $${y^2} = x.$$ Show that $$c$$ must be greater than $$1/2$$. One normal is always the $$x$$-axis. Find $$c$$ for which the other two normals are perpendicular to each other.
c > 1/4
c > 1/2
c < 1/2
c = 3/4 when the other two normals are perpendicular
The x-axis cannot be a normal