The equation of the line passing through the point of intersection of the lines $x-3 y+2=0$ and $2 x+5…
The equation of the line passing through the point of intersection of the lines $x-3 y+2=0$ and $2 x+5 y-7=0$ and perpendicular to the line $3 x+2 y+5=0$ is :
$2 x-3 y+1=0$
$6 x-9 y+11=0$
$2 x-3 y+5=0$
$3 x-2 y+1=0$
Solution
The equation of lines are
$x-3 y+2=0$ ...(i)
and $2 x+5 y-7=0$ ...(ii)
On solving Eqs. (i) and (ii), we get
$x=1, y=1$
$\therefore$ The co-ordinates of a point of intersection of given lines are $(1,1)$.
The equation of line perpendicular to $3 x+2 y+5=0$ is $2 x-3 y+\lambda=0$.
Which passes through $(1,1)$.
$\therefore \quad 2-3+\lambda=0$
$\Rightarrow \quad \lambda=1$
$\therefore$ Required equation of line is
$2 x-3 y+1=0$