Question

Find the combined equation- of pair of line passing
through the origin and perpendicular to the line x+5y-3=0
and 3x + y -1=0​

Answer 1

Equation of Line passing through (0,0) and perpendicular to the line x+5y-3=0 is

$5x - y = 0$

Similarly, for the line 3x+y-1=0:

$x - 3y = 0$

Multiplying both the equations of line to obtain the equation of pair of straight lines ATQ:

$(5x - y)(x - 3y) = 0$

$\boxed{5 {x}^{2} + 3 {y}^{2} - 16xy = 0}$