Question

Consider the family of lines $5x+3y-2+\lambda \left(3x-y-4\right)=0$ and $x-y+1+\mu \left(2x-y-2\right)=0$ . The equation of a straight line that belongs to both the families is

• A. $5x-2y-7=0$
• B. $3x+y-2=0$
• C. $5x+2y-3=0$
• D. $2x+y-1=0$

Answer 1

Answer: (A)

All lines of the family $5x+3y-2=0$ and $\left(3x-y-4\right)=0$ are concurrent.
The point of concurrency is $\left(1,-1\right)$
Similarly, the point of concurrency of lines of the other family is $\left(3,4\right)$
$\Rightarrow$ The line of both families is the line passing through $\left(1,-1\right)\&\left(3,4\right)$
$\Rightarrow$ Equation of the required line is $5x-2y-7=0$