If lines represented by 1 + s i n 2 θ x 2 + 2 h x y + 2 i s i n θ y 2 = 0 , θ ∈ 0,2 π are perpendicular to each other then θ = ….

Question

If lines represented by 1 + s i n 2 θ x 2 + 2 h x y + 2 i s i n θ y 2 = 0 , θ ∈ 0,2 π are perpendicular to each other then θ = …., π 2, π, 3 π 2, π 6

MARKS App · Accepted Answer

Key Idea Given, a x 2 + 2 h x y + b y 2 = 0 represents perpendicular pair of straight lines then a + b =0 We have, pair of lines represented by 1 + s i n 2 θ x 2 + 2 h x y + 2 x i n θ y 2 = 0 , θ ∈ 0,2 π ∴ 1 + s i n 2 θ + 2 s i n θ = 0 ⇒ 1 + s i n θ 2 = 0 ⇒ 1 + s i n θ = 0 ⇒ s i n θ = - 1 = - s i n π 2 = sin ⁡ 2 π - π 2 ⇒ s i n θ = s i n 3 π 2 ⇒ θ = 3 π 2

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