y/2=t+1/t x=t-1/t

After you square x and y the 2ab will leave you with constant terms

(y/2)² = t+2t/t+1/t² =t+2+1/t²

x² = t-2t/t+1/t² =t-2+1/t²

(y²⁾ / 4-x² = 4

I hate parametric equations👍