Question

The equation of the line with gradient $\frac{-3}{2}$ which is concurrent with the lines $4x+3y-7=0$ and $8x+5y-1=0$, is

• A. $3x+2y-2=0$
• B. $3x+2y-63=0$
• C. $2y-3x-2=0$
• D. None of these

Answer 1

The correct option is A $3x+2y-2=0$

The equation of a line concurrent with the lines $4x+3y-7=0$ and $8x+5y-1=0$ is
$(4x+3y-7)+\lambda (8x+5y-1)=0$
$\Rightarrow (4+8\lambda )x+(3+5\lambda )y-7-\lambda =0....\left(i\right)$
Given, the gradient of the line is $\frac{3}{2}$
$\therefore -\frac{8\lambda +4}{5\lambda +3}=\frac{3}{2}$
$\Rightarrow 16\lambda +8=15\lambda +9$
$\Rightarrow \lambda =1$
On putting $\lambda =1$ in Eq. (i), we get
$(4+8\times 1)x+(3+5\times 1)y-7-1=0$
$\Rightarrow 12x+8y-8=0$
or $3x+2y-2=0$.