Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If the chord joining the points whose eccentric angles are ‘ α ’ and ‘ β ’ on the hyperbola 
= 1 is a focal chord then
A
± ecos 
= cos 
= cos
B
± ecos 
= cos 
= cos
C
tan( α /2) tan( β /2) + 
= 0 where k = ± 1
= 0 where k = ± 1
D
tan( α /2) tan( β /2) + 
= 0 where k = ± 1
= 0 where k = ± 1
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,c,d)
(i) Points α and β on the hyperbola are (a sec α , b tan α ) and (a sec β , b tan β ).
Equation of chord joining α and β is
cos 
sin 
= cos 
By hypothesis this chord is focal chord and is passing through (± ae, 0)
∴ ± e cos 
= cos 
(ii) Let k = ± 1
∴ ke cos 
= cos 
= 
By componendo and dividendo method 
= 
⇒ tan 
tan 
+ 
= 0
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