- #1
AKJ1
- 43
- 0
Homework Statement
Problem that was gone over in class, but I missed part of the lecture
Describe all points (x,y) satisfying | p - s | + | p - t | = Q
where,
Vector p = <x,y>
Vector s = <a,b>
Vector t = <c,d>
a,b,c,d and Q are constants and Q is greater than | s - t |
The Attempt at a Solution
I think the graph is a cylinder, but I am having a lot of trouble trying to verify or describe that. I've tried writing in the components and brute forcing it, but it ends up quite hairy. I also have tried squaring both sides and using the fact that if u and v are vectors then
| u + v | ^2 = |u|^2 + |v|^2
But I haven't made much progress there either. Is there some identity or simplification I am not seeing?