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MHT CET202310 May 2023Evening ShiftMathematicsStraight LinesActual

The joint equation of a pair of lines passing through the origin and making an angle of 4 with the line 3 x+2 y-8=0 is

Options

  1. A5 x^2+24 x y-5 y^2=0
  2. B5 x^2-24 x y+5 y^2=0
  3. C5 x^2-24 x y-5 y^2=0
  4. D5 x^2+24 x y+5 y^2=0

Correct answer

A. 5 x^2+24 x y-5 y^2=0

Step-by-step solution

The slope of line 3 x+2 y-8=0 is m ₁= -3 2 Let m be the slope of one of the lines making an angle 4 with 3 x+2 y-8=0 aligned 4 & = | m - m ₁ 1+ mm ₁ | 1 & = | m - ( -3 2 ) 1+ m ( -3 2 ) | 1 & = | 2 ~m +3 2-3 ~m | aligned Squaring on both sides, we get aligned & (2-3 m)^2=(2 m+3)^2 & 5 m^2-24 m-5=0 aligned This is the auxiliary equation of two lines and their joint equation is obtained by putting m = y x The joint equation of the lines is gathered 5 ( y x )^2-24 ( y x )-5=0 i.e., 5 x^2+24 x y-5 y^2=0 gathered

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