Question

The value of $\lambda$ for which the lines joining the points of intersection of curves $C_{1}$ and $C_{2}$ to the origin are equally inclined to the axis of $x$, where $C_{2}$ : $\lambda x^{2}+3 y^{2}-2 \lambda x y+9 x=0$ and $C_{1}: 3 x^{2}-4 y^{2}+8 x y-3 x=0$, is

• A. $\quad \lambda=\frac{4}{3}$
• B. $\lambda=12$
• C. $\lambda=1$
• D. $\lambda=\frac{5}{6}$

Answer 1

Answer: (B)

To find the equation of pair of lines through origin we eliminate the terms containing $x$ from the equations of $C_{1}$ and $C_{2}$.
Thus, $C_{1}+3 C_{2}=0$
$ \Rightarrow (\lambda+9) x^{2}+(24-2 \lambda) x y-9 y^{2}=0$
These lines are equally inclined to axes if
$24-2 \lambda=0$ $ \Rightarrow \lambda=12$