My problem says find the surface area of the part of the surface

z=y^2-x^2 that is inside the cylinder x^2+y^2=2

So im thinking of polar coordinates

saying f(x,y)=y^2-x^2

and fx=-2x, fy=2y

and the area=

double integral of (sqrt(1+4x^2+4y^2))

but my problem is how to go about finding the limits

Im not sure exactly, can i get direction so i can learn