Question

Does curve r1(s)=(s^4/2-3s^2/4,s^2,3s/4) and r2(t)=(t^2-t,2t,t^2+t) intersect? If they do, in how many points do they intersect?

Answer 1

r1(s)=
x=s^4/2-3s^2/4
y=0+s^2,
z=0+3/4 s)

eww, how would we write this out in parametric vorm?

Answer 2

*form

Answer 3

i dont know

Answer 4

i was thinking to equalize cooeficient and then i get s=0,t=0 and put it in r1, r2, i get r1=(0,0,0)r2=(0,0,0) so they do intersect in one point

Answer 5

r_1(s)=r_2(t), iff
s^4/2-3s^2/4=t^2-t
s^2=2t
3s/4=t^2+t

Answer 6

Use equation(2) to find t in terms of s, then substitute that in either equation 1 or 3 to find s.

Answer 7

Make sure that the solution you get satisfy all three equations.

Answer 8

Here: http://www.wolframalpha.com/input/?i=s%5E4%2F2-3s%5E2%2F4%3Dt%5E2-t%2C+s%5E2%3D2t%2C+3s%2F4%3Dt%5E2%2Bt

Answer 9

The solutions are s=t=0 or s=1 and t=1/2. Plug that into r to find the coordinates of the points.