Find the common tangent`s equation to parabola y2=2x, x2=16y

General equation of a tangent Y=mx+a/m for the first given parabola, substitute the value of a ie a=1/2 we get an second degree equation in x ie mx2 - 16m2x - 8 =0 now we put the discriminant equal to zero to find the value of m after putting we get m=0 or m= - 5 but m cannot be zero, now plugging in the value of m in the first given equation we get the equation of tangent as 50x+ 10y +1 = 0Thank you this is my first answer sorry, if I had made any mistake.