Find the locus of the point P from which tangents are drawn to the parabola `y^(2) = 4ax` having slopes `m_(1)` and `m_(2)` such that
`m_(1)^(2)+m^(2)=lamda` (constant)
where` theta_(1)` and `theta_(2)` are the inclinations of the tangents from positive x-axis.

Explanation

Equation of tangent to
`y^(2)=4ax` is
`y=mx+a//m`
Let it passes through P(h, k).
`thereforem^(2)h-mk+a=0`
`m_(1)^(2)+m_(2)^(2)=lamda`
`!(k^(2))/(h^(2))-2a/h=lamda`
`therefore` locus of P(h, k) is
`y^(2)-2ax=lamdax^(2)`