Question

The equation of the straight line passing through the point of intersection of $5x-6y-1=0,3x+2y+5=0$ and perpendicular to the line $3x-5y+11=0$

• A. $5x+3y+18=0$
• B. $-5x-3y+18=0$
• C. $5x+3y+8=0$
• D. $5x+3y-8=0$

Answer 1

The correct option is C $5x+3y+8=0$

Given lines $5x-6y=1$ ....(1)
and $3x+2y+5=0$ ....(2)

Multiplying equation (2) by $3$, we get

$9x+6y=-15$ ....(3)
Adding equations (1) and (3), we get

$14x=-14\Rightarrow x=-1$

Putting this value in equation (2), we get

$-3+2y=-5$

$\Rightarrow y=-1$

Thus $(x,y)=(-1,-1)$
The equation of required line is $5x+3y+k=0$ and it is passing through $(-1,-1)$ is $-5-3+k=0$.
$\Rightarrow k=8$
Therefore, equation of line is $5x+3y+8=0$.