Question

The angle between the pair of straight lines 2x² - 6xy + y² = 0 is tan^-1 (p), where p = ______

Options

• `sqrt7/3`

• `7/11`

• `(2sqrt7)/3`

• `sqrt11/15`

Answer 1

The angle between the pair of straight lines 2x² - 6xy + y² = 0 is tan^-1 (p), where p = `underline((2sqrt7)/3)`.

Explanation:

Comparing the given equation with ax² + 2hxy + by² = 0, we get

a = 2, h = - 3, b = 1

∴ tanθ = `|(2sqrt(h^2 - ab))/(a + b)| = |(2sqrt(9 - 2))/3| = (2sqrt7)/3`

⇒ `theta = tan^-1((2sqrt7)/3)`

Given θ = tan^-1 (p)

∴ p = `(2sqrt7)/3`