Question

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

Options

• x² – x = 0

• xy – x = 0

• y² – x + 1 = 0

• xy + x + y + 1 = 0

Answer 1

y² – x + 1 = 0

Explanation:

(a) x² – x = 0

`\implies` x(x – 1) = 0

`\implies` x = 0 and x = 1,

This represent a pair of lines.

(b) xy – x = 0

`\implies` x(y – 1) = 0

`\implies` x = 0, y = 1,

This represent a pair of lines.

(c) y² – x + 1 = 0

`\implies` y² = (x – 1),

This represent a parabola.

Which does not represent a pair of lines.

(d) xy + x + y + 1 = 0

`\implies` x(y + 1) + (y + 1) = 0

`\implies` (y + 1)(x + 1) = 0

`\implies` y = –1 and x = –1

This represent a pair of lines.