Published by:
CGP EDU Academic Team
Published on: August 13, 2026
From any point on a hyperbola xy = c 2 tangents are drawn to another hyperbola xy = a 2 which has the same asymptotes. Then the chord of contact cuts off a constant area from the asymptotes:
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
A
Let xy = c 2 be the rectangular hyperbola referred to its asymptotes as the coordinate axis.
Let P(h, k) be a point on
xy = c 2 ... (i)
tangents are drawn from P(h, k) to the rectangular hyperbola xy = a 2 ∴ equation of chord of contact
⇒ kx + hy = 2a
2 This cuts the coordinate axis at A 
and B 
∴ Area of Δ OAB = 
= 
= 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
A point on the curve is
If the eccentricities of the hyperbolas and be e and , then
If P is a point on the hyperbola whose foci are and , then
If the latus rectum of an hyperbola be 8 and eccentricity be , then the equation of the hyperbola …
The eccentricity of a hyperbola passing through the points (3, 0), will be
The one which does not represent a hyperbola is