Question

An equation of a tangent to the hyperbola, $16 x^2-25 y^2-96 x+100 y-356=0$ which makes an angle $\frac{\pi}{4}$ with the transverse axis is $y=x+\lambda,(\lambda>0)$, then $2 \lambda$ is

• A. 16
• B. 4
• C. 3
• D. 9

Answer 1

Answer: (B)

Equation of the hyperbola can be written as $\frac{X^2}{5^2}-\frac{Y^2}{4^2}=1$
where $X=x-3$ and $Y=y-2$.
$\therefore $ tangent $Y=X \pm \sqrt{25-16}$
$\Rightarrow y=x+2$ or $y=x-4$