A) \[\left( \frac{1}{3},\frac{1}{4} \right)\]
B) \[\left( -\frac{1}{3},\frac{1}{4} \right)\]
C) \[\left( \frac{1}{3},-\frac{1}{4} \right)\]
D) None of these
Correct Answer: A
Solution :
Given, \[a+b+c=0\] ...(i) Line \[3ax+4by+c=0\] \[\Rightarrow \] \[3ax+4by-a-b=0\] [using Eq. (i)] \[\Rightarrow \] \[(3x-1)a+(4y-1)b=0\] Since, the lines passes through a fixed point \[\therefore \] \[3x-1=0,4y-1=0\] \[x=\frac{1}{3},y=\frac{1}{4}\] Hence, required point\[\left( \frac{1}{3},\frac{1}{4} \right)\].
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