The correct option is D m6+4m4+3m2+1=0
Equation of normal with slope ′m′ to the parabola y2=4ax is given by,
y=mx−2am−am3
Also this line touches the hyperbola x2−y2=a2
thus using condition of tangency to the hyperbola, c2=a2m2−b2
(−2am−am3)2=a2(m2−1)
⇒4m2+m6+4m4=m2−1
⇒m6+4m4+3m2+1=0
Hence, option 'D' is correct.