Question

The joint equation of the angle bisectors of the angles between the lines 4x² – 16xy + 7y² = 0 is ______.

विकल्प

• 8x² – 3xy + 8y² = 0

• 8x² + 3xy + 8y² = 0

• 8x² + 3xy – 8y² = 0

• 8x² – 3xy – 8y² = 0

Answer 1

The joint equation of the angle bisectors of the angles between the lines 4x² – 16xy + 7y² = 0 is 8x² – 3xy – 8y² = 0.

Explanation:

4x² – 16xy + 7y² = 0

Here a = 4,

b = 7,

h = –8

Equation of angle bisector is:

`(x^2 - y^2)/(a - b) = (xy)/h`

∴ `(x^2 - y^2)/-3 = (xy)/-8`

∴ 8x² – 8y² = 3xy

∴ 8x² – 3xy – 8y² = 0