Verified Solution • 2025–26 Session moderate

QJEEM24Ma7de6: JEE Main 2024 Mathematics - Class 11 JEEM24Ma7de6 Solution: If the locus of the point, whose distances from the point 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 :

Multiple Choice Options

  • A 37
  • B −27-27
  • C 437
  • D 5

Step-by-Step Verified Solution

JEE Main 2024 (Online) 6th April Evening Shift Mathematics - Straight Lines and Pair of Straight Lines Question 11 English Explanation

amp;∴(h−2)2+(k−1)2(h−1)2+(k−3)2=2516amp;h2+k2−4h−2k+5h2+k2−2h−6k+10=2516\begin{aligned}& \therefore \frac{(h-2)^2+(k-1)^2}{(h-1)^2+(k-3)^2}=\frac{25}{16} \\& \frac{h^2+k^2-4 h-2 k+5}{h^2+k^2-2 h-6 k+10}=\frac{25}{16} \\\end{aligned}

Replacing h→xh \rightarrow x and k→yk \rightarrow y .

amp;16x2+16y2−64x−32y+80amp;=25x2+25y2−50x−150y+250amp;9x2+9y2+14x−118y+170=0amp;⇒a=9,b=9,c=0,d=14,e=−118amp;a2+2b+3c+4d+eamp;81+18+56−118amp;⇒37\begin{aligned}& 16 x^2+16 y^2-64 x-32 y+80 \\& =25 x^2+25 y^2-50 x-150 y+250 \\& 9 x^2+9 y^2+14 x-118 y+170=0 \\& \Rightarrow a=9, b=9, c=0, d=14, e=-118 \\& a^2+2 b+3 c+4 d+e \\& 81+18+56-118 \\& \Rightarrow 37\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring