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MHT CET20249 May 2024Morning ShiftMathematicsPair of LinesActual

If an equation hxy + g x+ f y+ c =0 represents a pair of lines, then

Options

  1. Afg = ch
  2. Bgh = cf
  3. Cfh = cg
  4. Dhf =- cg

Correct answer

A. fg = ch

Step-by-step solution

Given equation of pair of lines is aligned & h x y+g x+f y+c=0 & A=0, B=0, C=c, F= f 2 , G= g 2 , H= h 2 aligned aligned & | array lll A & H & G H & B & F G & F & C array |=0 & | array ccc 0 & ~h 2 & ~g 2 ~h 2 & 0 & f 2 ~g 2 & f 2 & c array |=0 aligned aligned & -h 2 [ ch 2 - gf 4 ]+ g 2 [ hf 4 ]=0 & - h ^2 c 4 + hgf 8 + ghf 8 =0 & - h ^2 c 4 + hgf 4 =0 & ~h ^2 c = hgf & hc = gf aligned

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