Question

For what value of $\lambda$ does the line $y=3x+\lambda$ touch the hyperbola $9x^2-5y^2=45$.

• A. $\lambda =\pm 6$
• B. $\lambda =-6$
• C. $\lambda =6$
• D. none of these

Answer 1

The correct option is A $\lambda =\pm 6$

Given hyperbola may be written as, $\frac{x^2}{5}-\frac{y^2}{9}=1$
$\Rightarrow a^2=5,b^2=9,c=\lambda ,m=3$
Now using condition of tangency, $c^2=a^2{m}^2-b^2$
$\Rightarrow {\lambda }^2=5\times 9-9=36\Rightarrow \lambda =\pm 6$