question_answer

If   the   pair   of   straight   lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2qxy-{{y}^{2}}=0\] be such that each pair bisects the angle between the other pair, then     AIEEE  Solved  Paper-2003

A) \[p=q\]                                

B)       \[p=-q\]                              

C)       \[pq=1\]                             

D) \[pq=-1\]

Correct Answer: D

Solution :

The given equation is . On comparing with , we get Equation of the bisector of angles                     \[\Rightarrow \,\,\,\,\,\,\,\,\,{{x}^{2}}-{{y}^{2}}=-\frac{2\,xy}{p}\] \[\Rightarrow \]     \[{{x}^{2}}+\frac{2\,xy}{p}-{{y}^{2}}=0\]                              ... (i) But given equation of the bisector of angles is                                                ... (ii) On comparing Eqs. (i) and (ii), we get