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21/01/2022 2:16 pm
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Let A (secθ, 2tanθ) and B (secφ, 2tanφ), where θ + φ = π/2, be two points on the hyperbola 2x2 – y2 = 2. If (α, β) is the point of the intersection of the normals to the hyperbola at A and B, then (2β)2 is equal to ___________.
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21/01/2022 2:20 pm
Since, point A (sec θ, 2 tan θ) lies on the hyperbola
2x2 – y2 = 2
Therefore, 2 sec2 θ – 4 tan2 θ = 2
⇒ 2 + 2 tan2 θ – 4 tan2θ = 2
⇒ tan θ = 0 ⇒ θ = 0
Similarly, for point B, we will get φ = 0.
but according to question q + φ = π/2
which is not possible.