Question

The equation of the straight line perpendicular to $5x-2y=7$ and passing through the point of intersection of the lines $2x+3y=1$ and $3x+4y=6$, is

• A. $2x+5y+17=0$
• B. $2x+5y-17=0$
• C. $2x-5y+17=0$
• D. $2x-5y=17$

Answer 1

The correct option is A $2x+5y+17=0$

Let the equation of line which is perpendicular to

$5x-2y=7$ is $2x+5y=\lambda$ ...... $\left(i\right)$

The given lines are $2x+3y=1$ ...... $\left(ii\right)$ and $3x+4y=6$ ..... $\left(iii\right)$

Solving $\left(ii\right)$ and $\left(iii\right)$, we get

$x=14,y=-9$

$\therefore$ The point of intersection of given lines is $(14,-9)$

Since, the Eq. (i) is passing through the point $(14,-9)$

$\therefore 2\left(14\right)+5(-9)=\lambda \Rightarrow \lambda =-17$

$\therefore$ Eq. (i) becomes

$2x+5y+17=0$