Question

Show that the following equation represents a pair of lines.

x² + 2xy – y² = 0

Answer 1

Comparing the equation x² + 2xy – y² = 0 with

ax² + 2hxy + by² = 0, we get,

a = 1, 2h = 2, i.e. h = 1 and b = -1

homogeneous equation of second degree and h² – ab > 0, the given equation represents a pair of lines which are real and distinct.