Question

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

• A. $5 x + 3 y + 8 = 0$
• B. $3 x - 5 y + 8 = 0$
• C. $5 x + 3 y + 11 = 0$
• D. $3 x - 5 y + 11 = 0$

Answer 1

Answer: (A)

$5 x + 3 y + 8 = 0$

Answer 2

The point of intersection of $5 x - 6 y - 1 = 0$and $3 x + 2 y + 5 = 0$is $( - 1 , - 1 )$. Now the line perpendicular to $3 x - 5 y + 11 = 0$is $5 x + 3 y + k = 0$, but it passes through $( - 1 , - 1 )$ ⇒ $- 5 - 3 + k = 0 \Rightarrow k = 8$

Hence required line is $5 x + 3 y + 8 = 0$.