Given two functions (y=x^2+8 and y=x-6) how can I find the shortest distance between the two? And how do I find the points on these functions that are the least distance to the other? My teacher hinted that parameterizing the curves would help, but I still have no idea what to do...

I put the following into Maple (12) A := 2*x*z+2*z*y+x*y V := x*y*z sys := {A= S, diff(V, x) = lambda*(diff(A, x)), diff(V, y) = lambda*(diff(A, y)), diff(V, z) = lambda*(diff(A, z))} S being a constant solve(sys, [x, y, z, lambda]); and got: [[x = RootOf(3*_Z^2-S, label = _L1), y = RootOf(3*_Z^2-S, label = _L1), z = (1/2)*RootOf(3*_Z^2-S, label = _L1), lambda = (1/4)*RootOf(3*_Z^2-S, label = _L1)]] which makes no sense to me... How can I enter this system into maple and get an answer? (the system is gradA=gradV and A=S, S being a constant, which is shown above) Thanks!

I have the equation of a sphere x^2+y^2+z^2 = 36 and two points in three space P(-3,-10,2) and Q(5,14,8) and I need to show that the line between the points intersects the sphere graphically and analytically, but I cant even figure out how to graph them, and I have a suspicion, but am not sure, that to prove it analytically I would find the equation of the line in three space between the points and prove that the line equals the equation of the sphere in two places, but I cant figure out how to find that equation either.

I looked over the FAQ's and I was not doing anything wrong according to them but I have tried graphing all of the following and got blank graphs as a result every time. I am using Maple 12 on Mac OSX Leopard 10.5.4. plot3d((2*x^2+y^2)*e^(1-x^2-y^2), x = -1 .. 1, y = -1 .. 1, axes = normal, scaling = constrained, numpoints = 10000) implicitplot3d((2*x^2+y^2)*e^(1-x^2-y^2), x = -10 .. 10, y = -10 .. 10, z = -10 .. 10, axes = normal, scaling = constrained) implicitplot3d((z = 2*x^2+y^2)*e^(1-x^2-y^2), x = -10 .. 10, y = -10 .. 10, z = -10 .. 10, axes = normal, scaling = constrained)