Question

Show that the equation 2x² – xy – 3y² – 6x + 19y – 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan^-1 (5).

Answer 1

Comparing the given equation with general form we get a = 2, b = -3, c = - 20, f = 19/2, g = - 3, h = -1/2

The condition for the given equation to represent a pair of straight lines is 

The given equation represents a pair of straight lines.

The angle between the pair of straight lines is given by