Identify the conic represented by the parametric equations

Question

x=2^t+2^(-t)

y=2^t-2^(-t)

Answer 1

x+y=2^(t+1), x-y=2^(-t+1).

2^(t+1)×2^(-t+1)=2^2=4=(x+y)(x-y)=x²-y², so the equation of the conic is x²-y²=4 a hyperbola. However, there is no value for t for the left half of the hyperbola since x must always be positive.