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

• Correct answer
  A

  $2 x+5 y+17=0$
• B

  $2 x+5 y-17=0$
• C

  $2 x-5 y+17=0$
• D

  $2 x-5 y=17$

Solution

Let the equation of line which is perpendicular to $5 x-2 y=7$, is
On solving Eqs. (ii) and (iii), we get $x=14, y=-9$ Since the Eq. (i) is passing through the point $(14,-9)$ $\begin{aligned} \Rightarrow & & 2(14)+5(-9) & =\lambda \\ \Rightarrow & & 28-45 & =\lambda \\ \Rightarrow & \lambda & =-17 \end{aligned}$ $\therefore$ Equation (i) becomes $2 x+5 y=-17$ or $2 x+5 y+17=0$

Hence, the correct answer is option: 'A'.