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December 8th, 2016, 10:20 AM  #1 
Newbie Joined: Dec 2016 From: Tr Posts: 2 Thanks: 0  Curve equation ?
I am asked to write the equation of the curve which lies above the line y=2x and lies on the surface z=x^2+y^2 But this question seems not clear and proper. Because y=2x is a line in two dimensions and z=x^2+y^2 is the surface which is in 3 dimensional space. However, at least I should find curve equation which meets these conditions. I am really confused. btw, I should also represent this equation as w=f(x,y,z) function because after that I am going to find normal vector and tangent vector of that curve equation at some (x,y,z) point such as (1,2,5) 
December 8th, 2016, 03:55 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,110 Thanks: 1909 
(y, z) = (2x, 5x²) or (y  2x)² + (z  5x²)² = 0.

December 21st, 2016, 09:00 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895  Quote:
In order that (x, 2x, z) lie on $\displaystyle z= x^2+ y^2$, we must have $\displaystyle z= x^2+ (2x)^2= 5x^2$. So these points are of the form $\displaystyle (x, 2x, 5x^2)$. Quote:
Last edited by Country Boy; December 21st, 2016 at 09:18 AM.  

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