Let P be the point of intersection of the common tangents to the parabola y²=12x and the hyperbola 8x²-y²=8. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio?

Correct option is A. 5:4
Equation of tangents
y²=12x ⇒ y=mx+3/m
8x²-y²=8 ⇒ y=mx±√m²-8
Since they are common tangent
∴ 3/m=±√m²-8
9/m²=m²-8
m⁴-8m²-9=0
m²=9 or m²=-1 (rejected)
m=±3
∴ y=3x+1 and y=-3x-1
Intersection point P(-1/3, 0)
S=(√3,0), S'=(-√3,0)
The ratio in which P divides SS' is 5:4