Curve is represented parametrically by the equations \( x=t+e^{a t} \) and \( y=-t+e^{a t} \) wh...

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Curve is represented parametrically by the equations \( x=t+e^{a t} \) and \( y=-t+e^{a t} \) when \( t \in R \) and \( a0 \). If the curve touches the axis of \( x \) at the point \( A \), then the coordinates of the point \( \mathrm{A} \) are
(a) \( (1,0) \)
(b) \( (2 e, 0) \)
(c) \( (1 / e, 0) \)
(d) \( (e, 0) \)
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