Straight Line Question 53

Question: The straight lines $ 4ax+3by+c=0 $ where $ a+b+c=0 $ , will be concurrent, if point is [RPET 2002]

Options:

A)(4, 3)

B)(1/4, 1/3)

C)(1/2, 1/3)

D)None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • The set of lines is $ 4ax+3by+c=0 $ , where $ a+b+c=0 $ . Eliminating c, we get $ 4ax+3by-(a+b)=0 $
    Þ $ a(4x-1)+b(3y-1)=0 $ This passes through the intersection of the lines $ 4x-1=0 $ and $ 3y-1=0 $ i.e. $ x=\frac{1}{4},y=\frac{1}{3} $ i.e., $ ( \frac{1}{4},\frac{1}{3} ) $ .