(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a vector function that represents the curve of intersection of the two surfaces:

The cone z = sqrt( x^2 + y^2) and the plane z = 1+y.

2. Relevant equations

z = sqrt( x^2 + y^2) and the plane z = 1+y.

3. The attempt at a solution

This problem can be solved as following using x as the parameter.

x^2+y^2 = z^2 = (1+y)^2 = 1+2y+y^2. => x^2 = 1 + 2y.

x=t; y = (t^2-1)/2; z = 1+(t^2-1)/2 = (t^2+1)/2

My question is, what if we use y as the parameter,

i get ,

y=t, x=(2t+1)^(1/2) z=t+1,

is this answer also correct?

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# Find a vector function that represents the curve of intersection of the two surfaces

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