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Question: Answered & Verified by Expert
If a pair of lines $x^{2}-2 p x y-y^{2}=0$ and $x^{2}-2 q x y-y^{2}=0$ is such that each pair bisects the angle between the other pair, then
MathematicsPair of LinesMHT CETMHT CET 2011
Options:
  • A $p q=-1$
  • B $p q=1$
  • C $\frac{1}{p}+\frac{1}{q}=0$
  • D $\frac{1}{p}-\frac{1}{q}=0$
Solution:
1241 Upvotes Verified Answer
The correct answer is: $p q=-1$
Since, $x^{2}+\frac{2 x y}{p}-y^{2}=0$, is the angle bisectors of $x^{2}-2 p x y-y^{2}=0$
But given that angle bisectors are
$\therefore$
$$
\begin{array}{c}
x^{2}-2 q x y-y^{2}=0 \\
-2 q=2 / p
\end{array}
$$
$$
\Rightarrow \quad p q=-1
$$

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