Question

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

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

Answer 1

The correct option is C $\frac{9}{2}$

$2y{y}^{\prime }=16$

$y^{\prime }=\frac{8}{y}=m_1$

$y^{\prime }=\frac{-9x}{by}=m_2$

$m_1\cdot m_2=-1$

$\frac{8\times 9x}{b{y}^2}=1$

$b=\frac{9}{2}$