question_answer

If the pair of linesa\[{{x}^{2}}+2(a+b)xy+b{{y}^{2}}=0\] lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sector is thrice the area of another sector, then     AIEEE  Solved  Paper-2005

A) \[3{{a}^{2}}+2ab+3{{b}^{2}}=0\]

B) \[3{{a}^{2}}+10ab+3{{b}^{2}}=0\]

C) \[3{{a}^{2}}-2ab+3{{b}^{2}}=0\]

D) \[3{{a}^{2}}-10ab+3{{b}^{2}}=0\]

Correct Answer: A

Solution :

Equation of pair of lines is Since,                              ?.(i) Angle between lines is given by [from Eq. (i)]