Intersection of paraboloid and normal line

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Homework Help Overview

The problem involves finding the intersection of a normal line to the paraboloid defined by z=x^2+y^2 at a specific point (1,1,2) with the paraboloid itself, focusing on the second intersection point.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formulation of the normal line and its implications, with some questioning whether the derived equation represents a line or a plane. There is a suggestion to find points that satisfy both the normal line and the paraboloid equations.

Discussion Status

The discussion is ongoing, with participants providing guidance on clarifying the nature of the normal line and encouraging the original poster to share their work for further assistance. Multiple interpretations of the normal line's equation are being explored.

Contextual Notes

There is a mention of potential confusion regarding the nature of the equation derived by the original poster, as it may not align with the expected representation of a normal line.

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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.
 
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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.
 
Is there any you recommend I should try and do?
 
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.
 

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