Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If the tangent and the normal to a rectangular hyperbola at a point cut off intercepts a 1 , a 2 on one axis and b 1 , b 2 the other axis then a 1 a 2 + b 1 b 2 is equal to-
A
–1
B
0
C
1
D
Text Solution
Verified by ExpertsThe correct answer is:
B
Let the hyperbola be xy = c 2
Tangent at any point (ct, c/t)
x 
+ y = 0 ⇒ 
= – 
= – 
Equation of tangent ⇒ y – 
= 
(x – ct)
a 1 (Intercept on x-axis) ; 0 – 
= 
(x – ct)
a 1 = 2ct ; b 1 (Intercept of y-axis) ; b 1 = 2c/t
Equation of Normal ⇒ y – 
= t 2 (x – ct)
a 2 = 
, b 2 = 
⇒ a 1 a 2 + b 1 b 2 = 0
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