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JEE Main20246 Apr 2024Evening ShiftMathematicsStraight LinesActual

If the locus of the point, whose distances from the point (2,1) and (1,3) are in the ratio 5: 4 , is a x^2+b y^2+c x y+d x+e y+170=0 , then the value of a^2+2 b+3 c+4 d+e is equal to :

Options

  1. A37
  2. B437
  3. C-27
  4. D5

Correct answer

A. 37

Step-by-step solution

let P ( x , y ) aligned & (x-2)^2+(y-1)^2 (x-1)^2+(y-3)^2 = 25 16 & 9 x^2+9 y^2+14 x-118 y+170=0 & a^2+2 b+3 c+4 d+e & =81+18+0+56-118 & =155-118 & =37 aligned

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