The Combined Equation Of The Lines L1 and L2 is 2x2 + 6xy + y2 = 0 And That Of The Lines L3 and L4 is 4x2 + 18xy + y2 = 0. If The Angle Between L1and L4 be α, Then The Angle Between L2 and L3 will Be

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Question

The combined equation of the lines L₁ and L₂ is 2x² + 6xy + y² = 0 and that of the lines L₃ and L₄ is 4x² + 18xy + y²= 0. If the angle between L₁and L₄ be α, then the angle between L₂ and L₃ will be

easy

Solution

Correct option is

We observe that the combined equation of the bisectors of the angles between the lines in the first pair is

and that of the second pair is

Clearly, equations (i) and (ii) are same. Thus, the two pairs of lines have the same bisector. Consequently, they are equally inclined to each other. Hence, the angle between L₂ and L₃ is also α.