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MHT CET202415 May 2024Evening ShiftMathematicsStraight LinesActual

If one of the lines represented by a x^2+2 h x y+b y^2=0 is perpendicular to m x+ n y=18 , then

Options

  1. Aan ^2+2 hmn + bm ^2=0
  2. Bam ^2+2 hmn + bn ^2=0
  3. Cam ^2-2 hmn + bn ^2=0
  4. Dan ^2-2 hmn + bm ^2=0

Correct answer

B. am ^2+2 hmn + bn ^2=0

Step-by-step solution

Given equation of pair of lines is a x^2+2 ~h x y+ b y^2=0 aligned & a +2 ~h ( y x )+ b ( y x )^2=0 & a +2 hk + bk ^2=0 (i) aligned Now, slope of line m x+n y=18 is -m n Slope of the line perpendicular to m x+ n y=18 is k = n m Substituting the value of k in (i), we get aligned & a+2 h ( n m )+b ( n m )^2=0 & a^2+2 h m n+n^2=0 aligned

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