Which of the following equations in parametric form can represent a hyperbolic profile, where 't' is a parameter.
& y = 
− 
+ t = 0 & 
+ 
− 1 = 0
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a,c,d)
x = 
....(i) i.e. t + 
= 
y = 
....(ii) i.e. t – 
= 
adding 2t = 
+ 
t = 
+ 
= 
Put in (i) x = 
i.e. b 2 x 2 – a 2 y 2 = a 2 b 2
whereas represents an ellipse
x = e t + e – t .....(i)
y = e t – e –t
i.e. x + y = 2e t e t = 
put in (i)
x = 
+ 
i.e. y 2 – x 2 = 4 Hyperbola
x 2 – 6 = 2 cos t ⇒ y 2 + 2 = 4 cos 2 
= 2 (1 + cos t) = 2 
= 2 
y 2 + 2 = x 2 – 4 Hyperbola
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