Question

Normals are drawn from the point P with slope m₁, m₂, m₃ to the parabola y² = 4x. If locus of P with m₁m₂ = α is a part of the parabola itself, then find α.

Answer 1

We know, equation of normal to  y² = 4x is 

y = mx - 2am - am³ 

Thus, equation of normal to y² = 4x is,

y = mx - 2m - m³ ,let it passes through (h, k).