Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The slopes of common tangents to the hyperbolas
and 
are:
A
± ± 2
B
± ± 1
C
± ± 
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Given two hyperbolas are
... (i)
and 
... (ii)
Equation of tangent on equation (i)having slope m is
y = mx ± ± 
... (iii)
Eliminating y between equation (ii) and (iii) we get 16
(mx ± ± 
- 9x 2 = 144.
⇒ ⇒ (16m 2 - 9)x 2 ± ± 32m 
x + (144m 2 - 400) = 0 ... (iv)
For it to be tangent D = 0.
∴ ∴ (32m 
= 4 (16m 2 - 9) (144m 2 - 400)
⇒ ⇒ m 2 = 1 ⇒ ⇒ m = ± ± 1.
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