Question

If the distance between two parallel tangents drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{49}=1$ is $2$, then their slope is equal to

• A. $\pm \frac{5}{2}$
• B. $\pm \frac{4}{5}$
• C. $\pm \frac{3}{2}$
• D. None of these

Answer 1

The correct option is A $\pm \frac{5}{2}$

According to the question,
$\frac{2\sqrt{9m^2-49}}{\sqrt{1+m^2}}=2$
or $9m^2-49=1+m^2$
or $8m^2=50$
or $m=\pm \frac{5}{2}$