y² = 6x ,                         9x² + by² = 16

2y y' = 6                        18 x + 2by y' = 0

y' = $\frac{3}{{\mathrm{y}}_1}$                         y' =$\frac{-9{\mathrm{x}}_1}{\mathrm{b}{\mathrm{y}}_1}$ 

$\frac{3}{{\mathrm{y}}_1}\times \left(\frac{-9{\mathrm{x}}_1}{\mathrm{b}{\mathrm{y}}_1}\right)$ = –1

27 x₁ = b y₁²

27 x₁ = b. 6x₁

b = $\frac{9}{2}$   {$\because {\mathrm{x}}_1\ne 0$}.