Question

The joint equation of pair of straight lines passing through the origin and having slopes `1 + sqrt2` and `1/(1 + sqrt2)` is ______ 

Options

• x² + 2xy + y² = 0 

• x² + 2xy - y² = 0 

• `x^2 - 2sqrt2 xy + y^2 = 0`

• `x^2 - 2sqrt2 xy - y^2 = 0`

Answer 1

The joint equation of pair of straight lines passing through the origin and having slopes `1 + sqrt2` and `1/(1 + sqrt2)` is `underline(x^2 - 2sqrt2 xy + y^2 = 0)`.

Explanation:

Joint equation of pair of lines having slopes m₁ and m₂ and passing through the origin is `y^2 - (m_1 + m_2)xy + m_1m_2x^2 = 0`

⇒ `y^2 - (1 + sqrt2 + 1/(1 + sqrt2))xy + (1 + sqrt2)(1/(1 + sqrt2)) x^2 = 0`

⇒ `y^2 - (1 + sqrt2 + (sqrt2 - 1)/1)xy + x^2 = 0`

⇒ `x^2 - 2sqrt2xy + y^2 = 0`