Question

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

The paraboloid z=4x²+y² and the parabolic cylinder y=x².

Answer 1

The curve of intersection is a parabolic curve.

Step-by-step explanation:

To find the vector function that represents the curve of intersection of the two surfaces, we need to set the equations of the surfaces equal to each other. Setting z = 4x^2 + y^2 equal to y = x^2 gives us:

4x^2 + y^2 = x^2

3x^2 + y^2 = 0

From here, we can see that this equation reduces to the equation of a parabola in the x-y plane. Therefore, the curve of intersection is a parabolic curve.