The line through`P`, perpendicular to the chord of the tangents drawn from the point `P` to the parabola `y^(2)=16x` touches the parabola `x^(2)=12y`, then the locus of `P` is `2ax+3y+4a^(2)=0` then `a` is ________

Answer

4

Explanation

Let `P(x_(1),y_(1))` equation of chord of contact `yy_(1)=8(x+x_(1))`
Equation of line perpendicular to this and passes through `P` is `y-y_(1) =(-y_(1))/8(x-x_(1))` ltbr This touches `x^(2)=12y`
`implies` Locus is `8x+3y+64=0`