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What is the minimal distance?
The curve
x^2 - x y + y + 1 = 0
has two branches.
Consider a point A on one branch and B on the other branch. What is the minimal value of AB?
1 Answer
- nleLv 77 years agoFavorite Answer
The curve can be written as
y = (x^2 +1) / (x-1)
and the graph
http://i794.photobucket.com/albums/yy228/smith123c...
So use the distance formula
d^2 = (x1 -x2)^2 + (y1-y2)^2
Set the derivatives to zero or use Lagrange
x1 = -0.1892 , x2 = 2.1892
so the minimal distance is 6.215
( with the use of a software )
