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AP EAMCET20226 Jul 2022Evening ShiftMathematicsPair of LinesActual

The distance between the lines represented by 4 x^2+20 x y+25 y^2+2 x+5 y-12=0 is equal to

Options

  1. A7 29
  2. B0
  3. C7 29
  4. D49 29

Correct answer

A. 7 29

Step-by-step solution

aligned & 4 x^2+(20 y+2) x+ (25 y^2+5 y-12 ) & x= -(20 y+2) (20 y+2)^2-4 4 (25 y^2+5 y-12 ) 2 4 & x=-20 y-2 400 y^2+4+80 y-400 y^2 -80 y+192 & x= -20 y-2 14 8 8 x+20 y=-2 14 & 8 x+20 y-12=0 and 8 x+2 y+16=0 aligned The given two lines are parallel aligned d & = |16+12| 8^2+(20)^2 & = 28 64+400 = 28 464 = 7 29 aligned

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