Perpendiculars are drawn from two points on axis of parabola `y^2=4ax` to a tangent to the parabola. The two point are situated at a distance of d from focus. if the perpendicular distances from the points are `p_1` ND `P_2` THEN FIND THE VALUE OF `P_1^2`-`P_2^2`

Explanation

`y^2=4ax`

`y(2at)=2a(x+at^2)`

`ty=x+at^2`

`x-ty+at^2=0-(1)`

`P_1=(|(a+d)-0+at^3|)/sqrt(1+t^2)`

`P_2=(|(a-d)-0+at^3|)/sqrt(1+t^2)`

subtracting`P_2^2` from`P_1^2`

`=(a+d+at^2)^2/(1+t^2)-(a-d+at^2)^2/(1+t^2)`

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