Question

Part 1: A Space Curve Embedded on a Surface: (material HW1 & HW2) Space curve: *(t) = (2e+sin(t),6e2t, 2e*cos(t)) A: Find the equation of a quadric surface on which the given space curve is embedded. B: Show the space curve is embedded on this quadric surface. C: Draw a LARGE 3-D diagram of the quadric surface in color (shade BLUE) on an entire page in Landscape and sketch the space curve on the surface in RED for Ost <2nt, label t = 0,11, 21 and show the curve trace direction. Label FULLY! D: Find the equation of a tangent line to the space curve @t = 0 and draw this in GREEN on the diagram. Use s for its parameter.

Answer 1

1 ) n=aet sint y = beat 2- 2etlost a²+ z²= 4e2t (cast+-sin?) n²+2 [:cott sinht=1) e2t 11 4 = 3x²+ 3z²zzy 2) : . It is of the form + (2²+2 h2 72 + 2hzx 2+ dão + C, X+624 7132 a=? b = 3, C2=-2, rest are o zhty ax²+by When It is a quadratic Surface