trace the curve x^2y^2=a^2(y^2-x^2)?

Answer 1

Add (a^2-y^2).x^2 to both sides to get

a^2.x^2 = a^2.y^2 - x^2.y^2

Then divide by (a^2-x^2) and switch round to get

y^2 = a^2.x^2 / (a^2 - x^2)

Taking squre roots gives

y = +/- a.x / sqrt(a^2-x^2)