This preview shows page 1. Sign up to view the full content.
Unformatted text preview: th subtracted.
The answer is a hyperbola.
Definition 7.6. Given two distinct points F1 and F2 in the plane and a ﬁxed distance d, a
hyperbola is the set of all points (x, y ) in the plane such that the absolute value of the diﬀerence
of the distances between the foci and (x, y ) is d. The points F1 and F2 are called the foci of the
hyperbola. (x1 , y1 ) F1 F2
(x2 , y2 ) In the ﬁgure above:
the distance from F1 to (x1 , y1 ) − the distance from F2 to (x1 , y1 ) = d
the distance from F2 to (x2 , y2 ) − the distance from F1 to (x2 , y2 ) = d
Note that the hyperbola has two parts, called branches. The center of the hyperbola is the
midpoint of the line segment connecting the two foci. The transverse axis of the hyperbola is
the line segment connecting two opposite ends of the hyperbola which also contains the center and
foci. The vertices of a hyperbola are the points of the hyperbola which lie on the transverse axis.
In addition, we will show momentarily that there are lines called asymptotes which th...
View Full Document