JEE Math Practice Question

Let C1 be the curve obtained by the solution of differential equation $$2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0$$. Let the curve C2 be the solution of $${{2xy} \over {{x^2} - {y^2}}} = {{dy} \over {dx}}$$. If both the curves pass through (1, 1), then the area enclosed by the curves C1 and C2 is equal to :

1. A.$${\pi \over 4}$$ + 1
2. B.$$\pi$$ + 1
3. C.$$\pi$$ $$-$$ 1
4. D.$${\pi \over 2}$$ $$-$$ 1