Question

Let curve intersect each other at point P(x₁, y₁)
$y_1^2=6x_1$     ..... (i)
& $9x_1^2+by{ }_1^2=16$     ..... (ii)
Now differentiate both curve and get slope of
tangent to both curve at point P(x₁, y₁)
$\therefore {\left(\frac{dy}{dx}\right)}_{(x, y)}=m_1=\frac{3}{y_1}$   ..... (iii)
$\& {\left(\frac{dy}{dx}\right)}_{(x_1, y_1)}=m_2=\frac{9x_1}{b{y}_1}$      ..... (iv)
$\because$   m₁m₂ = - $\Rightarrow \frac{27x_1}{b{y}_1^2}=1$
$\therefore$ from equation (i) b = $\frac{9}{2}$