Q84 / 160 · TS EAMCET 2018 (05 May Shift 2) · Mathematics
The equation of the straight line which is perpendicular to the line $5 x-2 y=7$ and passing through the point of intersection of the lines $2 x+3 y-1=0$ and $3 x+4 y-6=0$ is
- A$2 x+5 y-17=0$
- Correct answerB$2 x+5 y+17=0$
- C$2 x+5 y+47=0$
- D$2 x+5 y-47=0$
Solution
We have,
$$
\begin{aligned}
& 2 x+3 y-1=0 \\
& 3 x+4 y-6=0
\end{aligned}
$$
Solving Eqs. (i) and (ii), we get
$$
x=14, y=-9
$$
Equation of line perpendicular to the line $5 x-2 y=7$ and passing through $(14,-9)$ is.
$$
\begin{gathered}
2 x+5 y=2(14)+5(-9) \\
2 x+5 y=28-45 \Rightarrow 2 x+5 y+17=0
\end{gathered}
$$
Hence, the correct answer is option: 'B'.