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MHT CET202124 Sep 2021Morning ShiftMathematicsPair of LinesActual

The joint equation of pair of lines through the origin and having slopes (1+ 2 ) and 1 (1+ 2 ) is

Options

  1. Ax^2+2 x y+y^2=0
  2. Bx^2-2 2 x y-y^2=0
  3. Cx^2-2 2 x y+y^2=0
  4. Dx^2+2 x y-y^2=0

Correct answer

C. x^2-2 2 x y+y^2=0

Step-by-step solution

1 1+ 2 = ( 2 -1) ( 2 +1)( 2 -1) = 2 -1 2-1 = 2 -1 Hence equations of lines passing through origin and having slopes ( 2 +1) and ( 2 -1) are y =( 2 +1) x and y =( 2 -1) x Their joint equation is [( 2 +1) x - y ][( 2 -1) x - y ]=0x^2-2 2 x y+y^2=0

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