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Homework Statement
Find a vector function that represents the curve of intersection of the two surfaces:
The paraboloid z = 4x^2 + y^2
The parabolic cylinder y = x^2
Homework Equations
z = 4x^2 + y^2
y = x^2
The Attempt at a Solution
Combining the two equations:
z = 4(sqrt(y))^2 + y^2
z = 4y + y^2
Choose a parameter:
Let y = t
z = 4t + t^2
Therefore:
x = sqrt(t)
y = t
I get the equation:
r(t) = (sqrt(t))i + (t)j + (4t + t^2)k
Is this correct or did I do something wrong?
Any help appreciated, thanks!