The correct option is A 1a
Let (at21,2at1) and (at22,2at2) be any two points on the given parabola
Equation of tangent to the parabola y2=4ax at (at21,2at1) is
t1y=x+at21
Since this tangent meets x-axis in P1.
Coordinates of P1 are (−at21,0)
Equation of tangent to the parabola y2=4ax at (at22,2at2) is
t2y=x+at22
Since, this tangent meets x-axis in P2.
Coordinates of P2 are (−at22,0)
SP1=a(1+t21);SP2=a(1+t22)
⇒t1t2=−1
1SP1=1a(1+t21)
1SP2=1a(1+t22)=t21a(t21+1)
∴1SP1+1SP2=1a