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AP EAMCET202124 Aug 2021Morning ShiftMathematicsStraight LinesActual

The distance between pair of parallel lines represented by x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0 is. units

Options

  1. A5 2
  2. B5 2 a
  3. C2 5 a
  4. Da

Correct answer

B. 5 2 a

Step-by-step solution

Given, x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0 represents a pair of parallel lines. Compare with standard form aligned & a x^2+b y^2+2 h x y+2 g x+2 f y+c=0 & a=1, b=1, h=1, g=-4 a, f=-4 a, c=-9 a^2 aligned We know that distance between the parallel lines. aligned D & =2 g^2-a c a(a+b) & =2 (-4 a)^2-(1) (-9 a^2 ) 1(1+1) & =2 16 a^2+9 a^2 2 =2 25 a^2 2 =2 5 a 2 =5 2 a aligned

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