Question

Find the equation of the line which passes through the point of intersection of the lines 2x - y + 5 = 0 and 5x + 3y - 4 = 0 and is perpendicular to the line x - 3y + 21 = 0

• A. 2x + y + 8 = 0
• B. 3x+ 4y - 7 = 0
• C. 3x+ y = 0
• D. none of these

Answer 1

The correct option is C 3x+ y = 0

Solving 2x - y + 5 = 0 and 5x + 3y - 4 = 0, we get x = - 1
and y = 3 i.e., the point of intersection of the given lines is (-1, 3).
$\therefore$ The equation of any line perpendicular to the line
x - 3y + 21 = 0 is 3x + y + k = 0......(1)
If this line (1) passes through the point (-1, 3), the required equation of the line is 3x + y = 0.