P(h,k) for a parabola $y^2=4ax$ is a co-normal point.
We know that for a parabola $y^2=4ax$ normal is given by
(h,k) will satisfy the equation.
This is cubic in m,so it has three roots $m_1,m_2,m_3$
equation(1),(2)&(3) are the three conditions.
Hence (d) is the correct answer.