If lines represented by 1+sin^2θx^2+2hxy+2isinθy^2=0,θ∈0,2π are perpendicular to each other then θ = …

Question

If lines represented by 1+sin^2θx^2+2hxy+2isinθy^2=0,θ∈0,2π are perpendicular to each other then θ = ….

MARKS Content Team · Accepted Answer

Correct answer: (C) (3π)/2. Key Idea Given, ax^2+2hxy+by^2=0 represents perpendicular pair of straight lines then a + b =0 We have, pair of lines represented by 1+sin^2θx^2+2hxy+2xinθy^2=0,θ∈0,2π ∴1+sin^2θ+2sinθ=0 ⇒1+sinθ^2=0 ⇒1+sinθ=0 ⇒sinθ=-1=-sin(π)/2=sin⁡2π-(π)/2 ⇒sinθ=sin(3π)/2⇒θ=(3π)/2

If lines represented by $(1 + {s i n}^{2} θ) x^{2} + 2 h x y + 2 i s i n θ y^{2} = 0, θ \in [0,2 π]$ are perpendicular to each other then $θ$ = ….

Solution

Relevant Questions

If lines represented by 1+sin2θx2+2hxy+2isinθy2=0,θ∈0,2π are perpendicular to each other then θ = ….

Solution

Relevant Questions

If lines represented by $(1 + {s i n}^{2} θ) x^{2} + 2 h x y + 2 i s i n θ y^{2} = 0, θ \in [0,2 π]$ are perpendicular to each other then $θ$ = ….