Curve of intersection of the surfaces
z = x3 and
y =sin x + z2
The curve can be parametrized as r(t) = < t, sin t + t6 , t3>
Curve of intersection of the surfaces
z = 3 x2 + y2 (elliptic paraboloid) and
y = x2 (parabolic cylinder)
The curve can be parametrized as r(t) = < t, t2 , 3t2 + t4>
Curve of intersection of the surfaces
x2 + y2 = 9 (cylinder) and
z = xy (hyperbolic paraboloid)
The curve can be parametrized as r(t) = < 3 cost , 3 sint , 9 cost sint >
Curve of intersection of the surfaces
x2 + z2 = 9 (cylinder) and
y = x2 + z
The curve can be parametrized as r(t) = < 3 cost , 9 cos2t + 3 sint , 3 sint >
Curve of intersection of the surfaces
2
2
z=  x  y (cone) and
z = 1 + y (plane)
The curve can be parametrized as r(t) = < t , (t2-1)/2 , 1 + (t2-1)/2 >
Curve of intersection of the surfaces
z = x2 + y2 (paraboloid) and
5x – 6y + z – 8 = 0 (plane)
2
5
93
The projection of the curve on the xy plane is the circle  x   y−32=
2
4
The curve can be parametrized as
2
2
5  93
93
5  93
93


r(t) = < − 
cos t , 3
sin t ,− 
cos t  3
sin t  >
2
2
2
2
2
2