Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A curve is represented parametrically by the equations x = t + e at and y = – t + e at when
r ∈ R and a > 0. If the curve touches the axis of x at the point A, then the coordinates of the point A are -
Text Solution
Verified by ExpertsThe correct answer is:
D
x = t + e at ; y = – t + e at 
= 1 + ae
at ; 
= – 1 + ae at
= 
At the point A, y = 0 and 
= 0 for some t = t 1
∴ 
= 1 …(i)
Also, 0 = – t 1 + 
; ∴ 
= t 1 …(ii)
On putting this value in Eq. (i), we get
at 1 = 1 ⇒ t 1 = 
;
Now, from Eq. (i), ae = 1 ⇒ a = 
Hence, x A = t 1 + 
= e + e = 2e
⇒ A ≡ (2e, 0).
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