Maths-
General
Easy

Question

If the pair of lines a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0 intersect on the x-axis, then 2fgh=

  1. a f squared plus ch squared
  2. bg squared plus ch squared
  3. af squared plus bg squared
  4. a f squared plus g squared

hintHint:

General synopsis of Pair of straight lines.

The correct answer is: a f squared plus ch squared


    Given That:
                        If the pair of lines a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0 intersect on the x-axis, then 2fgh=
     
    Put x = 0 in the given equation 
    =>by2+2fy+c=0

    For unique point of intersection. 
    Discriminant = 0
    f2bc=0
    => af2a*b*c=0
    Since abc+2fghaf2bg2ch2=0
    => 2fghbg2ch2=0
    2fgh=bg2+ch2
    >>> Therefore, we can say that 2fgh=bg2+ch2.

    2fgh=bg2+ch2
     

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