Consider the curve C parametrized by
x = (t^2 + 1)/(t^2 − 1) and y = (2t)/(t^2 − 1)
for all t in (−∞, −1 ) ∪ (−1, 1) ∪ (1, ∞) .
By squaring both x and y, find an equation of C in terms of just x and y (no t):
? - ? =1
x^2-y^2 = [(t^2+1)^2 - (2t)^2]/(t^2-1)^2 = (t^2-1)^2/(t^2-1)^2 = 1
x^2 - y^2 = 1
but only the left branch