Answer:
Option D
Explanation:
We have y2=6x
$\Rightarrow$ $2y\frac{\text{d}y}{\text{d}x}=6\Rightarrow \frac{\text{d}y}{\text{d}x}=\frac{3}{y}$
Slope of tangent at ( x1,y1) is m1 = $m_{1}=\frac{3}{y_{1}}$
Also , $9x^{2}+by^{2}=16$
$\Rightarrow$ $18x+2by\frac{\text{d}y}{\text{d}x}=0 \Rightarrow \frac{\text{d}y}{\text{d}x}=\frac{-9x}{by}$
Slope of tangent at ( x1,y1) is $m_{2}=\frac{-9x_{1}}{by_{1}}$
Since these are intersection at right angle
$\therefore$ $m_{1}m_{2}=-1\Rightarrow\frac{27x_{1}}{by^{2}_{1}}=1$
$\Rightarrow$ $\frac{27x_{1}}{6bx^{}_{1}}=1$ [$\because$ $y_{1}^{2}=6x_{1}$]
$\Rightarrow$ $b=\frac{9}{2}$
