MHT CET · Maths · Pair of Lines
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
- A \(p q=-1\)
- B \(p q=1\)
- C \(\frac{1}{p}+\frac{1}{q}=0\)
- D \(\frac{1}{p}-\frac{1}{q}=0\)
Answer & Solution
Correct Answer
(A) \(p q=-1\)
Step-by-step Solution
Detailed explanation
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
\(\therefore\) \(x^{2}-2 q x y-y^{2}=0\) \(-2 q=2 / p\)
\(\Rightarrow p q=-1\)
But given that angle bisectors are
\(\therefore\) \(x^{2}-2 q x y-y^{2}=0\) \(-2 q=2 / p\)
\(\Rightarrow p q=-1\)
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