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JEE Main 20199 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2019 · 9 January · Morning Shift · Mathematics · Straight Lines

Consider the set of all lines px + qy + r = 0 such that 3p + 2q +...

Consider the set of all lines px+qy+r=0px + qy + r = 0 such that 3p+2q+4r=0.3p + 2q + 4r = 0 . Which one of the following statements is true?

Options

  1. AThe lines are not concurrent.
  2. BThe lines are concurrent at the point (34,12)\left(\dfrac{3}{4}, \dfrac{1}{2}\right) .
  3. CThe lines are all parallel.
  4. DEach line passes through the origin.

Correct answer

B. The lines are concurrent at the point (34,12)\left(\dfrac{3}{4}, \dfrac{1}{2}\right) .

Step-by-step solution

Given condition is 3p+2q+4r=03p + 2q + 4r = 0

⇒34p+12q+r=0.......(1)⇒ \dfrac{3}{4}p + \dfrac{1}{2}q + r = 0 . . . . . . . \left(1\right)

And given family of line is px+qy+r=0...(ii)px + qy + r = 0 . . . ( ii )

From (i)( i ) we can say that equation (ii)( ii ) always passes through \left(\dfrac{3}{4}, \dfrac{1}{2}\right).<br/><br/>Hencealllinesareconcurrentat(34,12).<br /><br />Hence all lines are concurrent at \left(\dfrac{3}{4}, \dfrac{1}{2}\right) .
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