Curve equation ? lies above line y=2x, on the surface z=x^2+y^2

[kejinatsu]

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.

 

[Deleted member 4993]

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.

You can think of y=2x as the equation of the plane that contains the z-axis and the line y=2x.

 

[kejinatsu]

You can think of y=2x as the equation of the plane that contains the z-axis and the line y=2x.

I understand but how can I 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)