AP EAMCET · Maths · Pair of Lines
If pairs of straight lines \(x^2-2 p x y-y^2=0\) and \(x^2-2 q x y-y^2=0\) be such that each pair bisects the angle between the other pair, then
- A \(p q=1\)
- B \(p q=2\)
- C \(p q=-2\)
- D \(p q=-1\)
Answer & Solution
Correct Answer
(D) \(p q=-1\)
Step-by-step Solution
Detailed explanation
Equation of angle bisector for \(\begin{array}{rlrl} a x^2+2 h x y+b y^2 & =0 \\ \Rightarrow & \frac{x^2-y^2}{a-b} & =\frac{x y}{h} \end{array}\) and for \(x^2-2 p x y-y^2=0\) \(\Rightarrow \quad \frac{x^2-y^2}{1-(-1)}=\frac{x y}{-p} \Rightarrow x^2-y^2+\frac{2 x y}{p}=0\) Given…
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