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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2014 · 12 April · Online · Mathematics · Straight Lines

If the three distinct lines x+2 a y+a=0, x+3 b y +b=0 and x+4 a...

If the three distinct lines x+2ay+a=0,x+3byx+2 a y+a=0, x+3 b y +b=0+b=0 and x+4ay+a=0x+4 a y+a=0 are concurrent, then the point (a,b)(a, b) lies on aa :

Options

  1. Acircle
  2. Bhyperbola
  3. Cstraight line
  4. Dparabola

Correct answer

C. straight line

Step-by-step solution

x+2ay+a=0x+3by+b=0x+4ay+a=0\begin{aligned} &x+2 a y+a=0 \\ &x+3 b y+b=0 \\ &x+4 a y+a=0 \end{aligned} Subtracting equation (3) from (1) −2ay=0ay=0⇒y=0\begin{aligned} &-2 a y=0 \\ &a y=0 \Rightarrow y=0 \end{aligned} Putting value of yiny inequation (1), we get x+0+a=0x=−a\begin{aligned} &x+0+a=0 \\ &x=-a \end{aligned} Putting value ofxandyinx and y inequation (2), we get −a+b=0a=b\begin{aligned} &-a+b=0 \\ &a=b \end{aligned} Thus,(a,b)(a, b) lies on a straight line
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