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JEE Main20199 Jan 2019Morning ShiftMathematicsStraight LinesActual

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 statements is true?

Options

  1. AThe lines are not concurrent.
  2. BThe lines are concurrent at the point 3 4 , 1 2 .
  3. CThe lines are all parallel.
  4. DEach line passes through the origin.

Correct answer

B. The lines are concurrent at the point 3 4 , 1 2 .

Step-by-step solution

Given condition is 3 p + 2 q + 4 r = 0 ⇒ 3 4 p + 1 2 q + r = 0       . . . . . . . 1 And given family of line is p x + q y + r = 0   . . . ( i i ) From ( i ) we can say that equation ( i i ) always passes through 3 4 , 1 2 . Hence all lines are concurrent at 3 4 , 1 2 .

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