Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?
JEE · Math · previous-year question
- A.The lines are not concurrent
- B.The lines are concurrent at the point $$\left( {{3 \over 4},{1 \over 2}} \right)$$correct
- C.The lines are all parallel
- D.Each line passes through the origin
Answer
B. The lines are concurrent at the point $$\left( {{3 \over 4},{1 \over 2}} \right)$$
Explanation
Equation of lines; px + qy + r = 0 . . . . . (1) Also given 3p + 2q + 4r = 0 . . . . . . (2) divide equation (2) by 4, we get $${3 \over 4}P + {2 \over 4}q + r = 0$$ . . . . (3) By comparing (1) and (3) we get, x = $${3 \over 4}$$ and y = $${2 \over 4}$$ = $${1 \over 2}$$ For any value of p,q and r, the equation of set of lines will pan through $$\left( {{3 \over 4},{1 \over 2}} \right)$$
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