Question

If lines represented by (1 + sin²θ)x² + 2hxy + 2 sin θ y² = 0, θ ∈ [0, 2π] are perpendicular to each other then θ = _______.

पर्याय

• `pi/2`

• `pi`

• `(3pi)/2`

• `pi/6`

Answer 1

If lines represented by (1 + sin²θ)x² + 2hxy + 2 sin θ y² = 0, θ ∈ [0, 2π] are perpendicular to each other then θ = `underline((3pi)/2)`.

Explanation:

Given, ax² + 2hxy + by2 = O represents perpendicular pair of straight lines then a + b = 0

we have, pair of lines represented by

(1 + sin² θ)x² + 2hxy + 2 sin θ y² = 0, θ ∈ [0, 2π]

∴ (1 + sin² θ) + 2 sin θ = 0

⇒ (1 + sin θ)² = 0

⇒ 1 + sin θ = 0

⇒ sin θ = - 1 = - `sin pi/2 = sin (2pi - pi/2)`

⇒ sin θ = sin `(3pi)/2`

`=> theta = (3pi)/2`