Question

Which of the following equation does not represent a pair of lines?

Options

• x² + y² + 2xy - 1 = 0

• x² - y² - x = 0

• x² - y² - 2y - 1 = 0

• 15xy + 10x + 6y + 4 = 0

Answer 1

x² - y² - x = 0

Explanation:

Consider option (x² - y² - x = 0),

Given equation is x² - y² - x = 0

∴ a = 0, b = -1, c = 0, f = 0, g = ${\displaystyle \frac{-1}{2},h=0}$

Now, abc + 2fgh - af² - bg² - ch²

= 0 + 0 - 0 - ${\displaystyle \left(\frac{1}{4}\right)-0=\frac{-1}{4}\ne 0}$

∴ The equation does not represent a pair of straight Lines.