HyperbolaHard
Question
From any point on the hyperbola H1 : (x2 / a2) - (y2 / b2) = 1 tangents are drawn to the hyperbola H2 : (x2 / a2) - (y2 / b2) = 2. The area cut-off by the chord of contact on the asymptotes of H2 is equal to -
Options
A.ab/2
B.ab
C.2 ab
D.4 ab
Solution
Let any point on hyperbola H1 is (a sec θ, b tan θ).
Equation of chord of contact is
sec θ - 
tan θ = 2 ... (i)
Equation of asymptotes is y = ±
x ... (ii)
From (i) & (ii) we get two intersection point
P(2a (sec θ + tan θ), 2b (sec θ + tan θ))
Q (2a (sec θ - tan θ), - 2b (sec θ - tan θ))
Then area of triangle OPQ is ᐃ = 2ab.
Equation of chord of contact is
sec θ - tan θ = 2 ... (i)Equation of asymptotes is y = ±
x ... (ii)From (i) & (ii) we get two intersection point
P(2a (sec θ + tan θ), 2b (sec θ + tan θ))
Q (2a (sec θ - tan θ), - 2b (sec θ - tan θ))
Then area of triangle OPQ is ᐃ = 2ab.
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