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Three Dimensional Geometry
Question
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If one of the lines of my2+ (1 − m2)xy − mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is

  • −1/2

  • -2

  • 1

  • 2

Answer

C.

1

Equation of bisectors of lines xy = 0 are y = ± x
put y = ± x in my2+ (1 − m2)xy − m = 0,
we get (1 − m2) x2 = 0
⇒ m = ± 1

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If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.