If the curves y2=6x and 9x2+by2=16 intersect each other at right angles, then the value of b is

It is given that the curves y2=6x and 9x2+by2=16 intersect at right angles.
Let the slope of y2=6x be m1
Also, let the slope of 9x2+by2=16 be m2
Thus, we have m1m2=-1
Differentiating both the equations w.r.t x we get
2ydy/dx=6
Or, ym1=3 (1)
Also, 18x+2bydy/dx=0
Or, m2=-9x/by
We know that m1m2=-1
Thus, 3y × -9x/by = -1
→ b = 27xy2
Putting y2=6x in the above equation we get
b=27x(6x) = 92