**
Hyperbola
**

*
Hyperbola
.
Focuses
.
Equation of hyperbola.
*
*
Focal length.
*

*
Real and imaginary axes of
hyperbola. Eccentricity.
*

*
Asymptotes of hyperbola. Equation
of tangent line to hyperbola.
*

*
Tangency condition of straight
line and hyperbola.
*

**
A
hyperbola
**
(
Fig.1
) is
called a locus of points, a modulus of difference of distances from which to the
two given points

*F*

_{ 1 }and

*F*

_{ 2 }, called

**of hyperbola, is a constant value.**

*focuses*

**
An
equation of hyperbola
**
(
Fig.1
) is
:

Here the origin of coordinates is a center of symmetry of hyperbola, and the coordinate axes are its axes of symmetry.

The segment
*
F
*
_{
1
}
*
F
*
_{
2
}
= 2
*
ñ
*
,
where
is
called
**
a focal length
**
.
The segment

*AB*= 2

*a*is called

**of hyperbola, the segment**

*a real axis**CD*= 2

*b*is called

**of hyperbola. The number**

*an imaginary axis**e*=

*c*/

*a*,

*e*> 1 is called

**of hyperbola. The straight lines**

*an eccentricity*

*y*= ± (

*b / a*)

*x*are called

**.**

*asymptotes of hyperbola*
Let
*
Ð
*
(
*
õ
*
_{
1
}
,
*
ó
*
_{
1
}
) be
a point of hyperbola, then
**
an equation of tangent line to hyperbola
**
in
this point is:

**
A
tangency
condition
of
a
straight line
**

*y*=

*m x*+

*k*

*and a hyperbola**õ*

^{ 2 }/

^{ }

*a*

^{ 2 }–

*ó*

^{ 2 }/

*b*

^{ 2 }= 1 :

*
k
*
^{
2
}
=
*
m
*
^{
2
}
*
a
*
^{
2
}
*
*
–
*
*
*
b
*
^{
2
}
.