Intersection of paraboloid and normal line

[Lute]

Homework Statement

Where does the normal line to the paraboloid z=x^2+y^2 at the point (1,1,2) intersect the paraboloid a second time?

Homework Equations

The Attempt at a Solution

I found the normal line to be 0=2x+2y-1, but I'm not sure what to do next.

 

[phinds]

find the two points that satisfy both equations

However, a quick look at your line equation suggests to me that it is the equation of a plane that is normal to the xy plane so the solution would be a 2D parabola; not what you're looking for.

 

[Lute]

Is there any you recommend I should try and do?

 

[phinds]

first find the LINE asked for, not a plane (which isn't what was asked for) and then do what I suggested in post #2

EDIT: you say you have found the line. Post your work so we can help you see where you went wrong and got a plane instead.