Question

Find the equation of the straight line passing through intersection of the straight lines 5x – 6y = 1 and 3x + 2y + 5 = 0 and perpendicular to the straight line 3x – 5y + 11 = 0.

Answer 1

Equation of line through the intersection of straight lines 5x – 6y = 1 and 3x + 2y + 5 = 0 is 

5x – 6y – 1 + k (3x + 2y + 5) = 0 

x (5 + 3k) + y (-6 + 2k) + (-1 + 5k) = 0 

This is perpendicular to 3x – 5y + 11 = 0 

That is, the product of their slopes is -1