Question

If the curves $y^2=6x,9x^2+b{y}^2=16$ intersect each other at right angles, then the value of b is :

• A. 6
• B. $\frac{7}{2}$
• C. 4
• D. $\frac{9}{2}$

Answer 1

Answer: (D)

$y^2=6x;$ slope of tangent at $\left(x_1,y_1\right)$ is $m_1=\frac{3}{y_1}$
also $9x^2+b{y}^2=16;$ slope of tangent at $\left(x_1,y_1\right)$ is
$m_2=\frac{-9x_1}{b{y}_1}$
As $m_1{m}_2=-1$
$\Rightarrow \frac{-27x_1}{b{y}_1^2}=-1$
$\Rightarrow b=\frac{9}{2}($ as $y_1^2=6x_1)$