Question

Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair of the angle bisectors of the lines x² – 4xy – 5y² = 0 is ______.

Options

• x² – 3xy + y² = 0

• x² + 4xy – y² = 0

• x² + 3xy – y² = 0

• x² – 3xy – y² = 0

Answer 1

Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair of the angle bisectors of the lines x² – 4xy – 5y² = 0 is `underlinebb(x^2 + 3xy - y^2 = 0)`.

Explanation:

If equation of pair of st. line are ax² + 2hxy + by² = 0 then pair of angle bisector are `(x^2 - "y"^2)/("a" - "b") = (x"y")/"h"`.

Here a = 1, b = –5 and h = –2

∴ Pair of angle bisector are : `(x^2 - "y"^2)/(1 + 5) = (x"y")/(-2)`

⇒ x² – y² + 3xy = 0