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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Straight Lines

If the locus of the point, whose distances from the point (2,1) and...

If the locus of the point, whose distances from the point (2,1)(2,1) and (1,3)(1,3) are in the ratio 5:45: 4, is ax2+by2+cxy+dx+ey+170=0a x^2+b y^2+c x y+d x+e y+170=0, then the value of a2+2b+3c+4d+ea^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)\mathrm{P}(\mathrm{x}, \mathrm{y})(x−2)2+(y−1)2(x−1)2+(y−3)2=25169x2+9y2+14x−118y+170=0a2+2b+3c+4d+e=81+18+0+56−118=155−118=37\begin{aligned} & \frac{(x-2)^2+(y-1)^2}{(x-1)^2+(y-3)^2}=\frac{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 \end{aligned}$$
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