HyperbolaMedium
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.
Create a free account to view solution
View Solution FreeMore Hyperbola Questions
If the tangent at the point (2 sec θ, 3 tan θ) of the hyperbola is parallel to 3x − y + 4 = 0, then the ...Area of triangle formed by tangent to the hyperbola xy = 16 at (16, 1) and co-ordinate axes equals -...If PQ and PR are tangents drawn from a point P to the hyperbola = 1. If equation of QR is 4x − 3y − 6 = 0, t...The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0) The possible equation of the hyp...For the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{3} = 1$ the incorrect statement is :...