eliminate parameter t when

Question

x= ln(sqrt(1+t^2)+t) and y = sqrt(t^2+1)

Answer 1

e^x = sqrt(t^2+1) + t
e^x = y + t
but
y^2 = t^2+1
t^2 = y^2-1
t = sqrt (y^2-1)
so

e^x = y + sqrt(y^2-1)