If m is the slope of the common normal, then the equation of normal to parabola y2=4b(x−c) is given by
y=m(x−c)−2bm−bm3 ⋯(1)
Equation of normal to parabola y2=8ax is
y=mx−4am−2am3 ⋯(2)
From equations (1) and (2), we get
m(x−c)−2bm−bm3=mx−4am−2am3
⇒m2(2a−b)=c−2(2a−b)
⇒m2=c2a−b−2∵m2≥0⇒c2a−b−2≥0
∴c2a−b≥2 ⋯(3)
Hence (1,1,3) satisfies equation (3)