Question

Find the equation of the line passing through the point $(-4,5)$ and the point of intersection of the lines $4x-3y+7=0$ and $2x+3y+5=0$.

• A. $7x-8y+16=0$
• B. $7x+8y-16=0$
• C. $8x-3y-17=0$
• D. $8x+3y+17=0$

Answer 1

Answer: (D)

The given lines are
$4x-3y+7=0\dots (i)$
and $2x+3y+5=0\dots (ii)$
The equation of the family of lines passing through the intersection of the lines $(i)$ and $(ii)$ is
$(4x-3y+7)+k(2x+3y+5)=0\dots (iii)$
where $k$ is a parameter.
Since, it passes through $(-4,5)$, we have
$4\times (-4)-3\times 5+7+k\{2\times (-4)+3\times 5+5\}=0$
$\Rightarrow -16-15+7+k(-8+15+5)=0$
$\Rightarrow -24+12k=0$
$\Rightarrow k=2$
Substituting this value of $k$ in $(iii)$, the equation of the required line is
$(4x-3y+7)+2(2x+3y+5)=0$
$\Rightarrow 8x+3y+17=0$