Question

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

Options

• `x^2 - 2sqrt2"xy" + "y"^2 = 0`

• `x^2 - 2sqrt2"xy" - "y"^2 = 0`

• `x^2 + 2"xy" - "y"^2 = 0`

• `x^2 + 2"xy" + "y"^2 = 0`

Answer 1

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

Explanation:

Required equation of pair of straight lines passing through origin and having slopes,

`"m"_1 = (1 + sqrt2) and "m"_2 = 1/(1 + sqrt2) = sqrt2 - 1`

`=> ["y" - (1 + sqrt2)x]["y" - (sqrt2 - 1) x] = 0`

`=> "y"^2 - (sqrt2 - 1)"xy" - (1 + sqrt2)xy + (2 - 1)x^2` = 0

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

`=> "y"^2 - 2sqrt2 x"y" + x^2` = 0