Parametrize the curve of intersection of the surfaces (a paraboloid and a plane).

z = -x^2 - y^2

y = x

I feel like the answer is

x = t

y = t

z = -t^2 - t^2 = -2t^2

<t, t, -2t^2>

but that doesn't seem right to me for some reason.. if this is incorrect can someone tell me why or show me how..