Consider the set of all lines p x + q y + r = 0 such that 3 p + 2 q + 4 r = 0 . Which one of the following…

Consider the set of all lines px+qy+r=0 such that 3p+2q+4r=0. Which one of the following statements is true?
  1. The lines are not concurrent.
  2. The lines are concurrent at the point 34,12 .
  3. The lines are all parallel.
  4. Each line passes through the origin.

Solution

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

⇒34p+12q+r=0   .......1

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

From (i) we can say that equation (ii) always passes through 34,12 .

Hence all lines are concurrent at 34,12 .

Asked in: JEE Main 2019 (09 Jan Shift 1)

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