Question

The diameter of $16x^2-9y^2=144$ which is conjugate to $x=2y$ is

• A. $y=\frac{16}{9}x$
• B. $y=\frac{32}{9}x$
• C. $x=\frac{16}{9}y$
• D. $x=\frac{32}{9}y$

Answer 1

Answer: (B)

We know that $y=m_{1}x,y=m_{2}x$ are conjugate diameters to $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ if $m_1{m}_2=\frac{b^2}{a^2}$
Here hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$
$\therefore a^2=9,b^2=16$and $m_1=\frac{1}{2}$
$\therefore \frac{1}{2}\left(m_2\right)=\frac{16}{9}$
$\Rightarrow m_2=\frac{32}{9}$
$\therefore$ reqd. diameter is $y=\frac{32}{9}x$