how to find limits of integration in terms of r when a paraboloid intersects a plane

Question

I don't know how to find limits of integration in terms of r when a paraboloid intersects a plane. I have the equations

$z=1-x^2-y^2$ and $z=-2$

and i set $-2=1-x^2-y^2$

to get $x^2 + y^2 = -1$

but that has a negative radius. I also used a 3d graphing calculator and noticed they intersect a little bit under the radius 2, but I don't know what to use for the exact value. I tried radius = $\sqrt2$ but the answer came out wrong. Can someone explain this process for me? on how to find the radius of any plane intersecting a paraboloid?

edit: i see now that i messed up my signs, but when i do the integration my answer still comes up wrong. I think I'm doing something profoundly wrong. Can someone show me the whole process of finding the area of this surface? or do i have to make a new thread? the problem is below. Nevermind i got it.

Answer 1

From $-2=1-x^2-y^2$, move $-2$ to the right side and $-x^2-y^2$ to the left. Don't forget to change sign. You should have $x^2+y^2=3$

Answer 2

Setting the values of $z$ from two equations you should get $r=0$ to $r=\sqrt3$