Find a Tangent Plane Parallel to x+2y+3z=1 on the Curve y=x2+z2

[TheColorCute]

I'm completely lost on this question, and it's due tomorrow morning. Help?

Homework Statement

What point on y=x²+z² is the tangent plane parallel to the plane x+2y+3z=1?

Homework Equations

y=x²+z²
x+2y+3z=1

The Attempt at a Solution

I have no idea what to do...

Thanks!

 

[HallsofIvy]

The gradient of the function F(x,y,z) is always perpendicular to the surface F(x,y,z)= constant at the point (x,y,z). Now, do you know how to find the equation of a plane, given a normal vector and one point on that plane?