I have the following question and i'm lost:
Find a Hyperboloid of one sheet ( x^2/a^2 + y^2/b^2 - z^2/c^2 =1 ) that includes the line which connects the dots (0,1,1) and (1,0,-1)
I'm sorry but I don't quite follow your logic.
Isn't the line joining the points should be (x-x1/x2-x1)=(y-y1/y2-y1)=(z-z1/z2-z1) ?
and say I substitute into the hyperboloid the x,y,z... all I get is a mess, I still need to find the parameters a,b,c and on the of that the Lambda. And it looks very ugly
Well, what can it be? The Hyperboloid exists, it is defined in my HW assignment, I just need to find it
I checked carefully for typos, and can't seem to track any.
Is there maybe another way to approach the problem? Say if i substitute the 2 given points in the generic equation, I get 2 equations, and I only need to find one more- how can I find something else to give me another equation?
Thanks a bunch CB
If it's not any trouble, can you explain (or link to an explanation) about the initial step when you found the line joining the points using X(lambda)=LAMBDA*p1 + (1-LAMBDA)*p2? where did this come from? We never discussed such forms in our classes.