Question

The equation 3x² - 4xy + y² = 0 represent a pair of straight lines whose slopes differ by ______.

Options

• 2

• 3

• `1/6`

• `1/2`

Answer 1

The equation 3x² - 4xy + y² = 0 represent a pair of straight lines whose slopes differ by 2.

Explanation:

Given equation of lines is

3x² - 4xy + y² = 0

⇒ 3x² - 3xy - xy + y² = 0

⇒ 3x(x - y) - y(x - y) = 0

⇒ (x - y)(3x - y) = 0

⇒ x - y = 0  and  3x - y = 0

i.e., y = x  and y = 3x

∴ Slopes of lines are l and 3 respectively.

∴ Difference in slopes = 3 - 1 = 2