Find k if the equation x2 – y2 + 2x + 2y + k = 0 represents a pair of lines.
Comparing the given equation with ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 we get
a = 1, b = –1, c = k, f = 1, g = 1, h = 0.
Since the given equation represents a pair of lines. abc + 2fgh – af2 – bg2 – ch2 = 0.
=> 1(–1)k + 2(1)(1)(0) – (1)2 – (–1)(1)2 – k(0)2 = 0 => k = 0.