Find the locus of point whose chord of contact w.r.t. to the parabola `y^(2) = 4bx` is the tangent of the parabola `y^(2) = 4ax`.

Explanation

Equation of tangent to `y^(2) = 4ax` is
`y=mx+a/m` …(i)
Let it is chord of contact for parabola `y^(2) = 4bx` w.r.t. the point P(h, k)
`therefore` Equation of chord of contact is
yk = 2b(x + h)
`!y=(2b)/kx+(2bh)/k` …(ii)
From (i) & (ii),
`m=(2b)/k,a/m=(2bh)/k`
`!a=(4b^(2)h)/(k^(2))`
`therefore` locus of P is `y^(2)=(4b^(2))/ax`