**
Parabola
**

*
Parabola. Focus. Directrix.
Equation of parabola.
*

*
Equation of tangent line to
parabola.
*

*
Tangency condition of straight
line and parabola.
*

**
A parabola
**
(
Fig.1
) is called a locus of
points, equidistant from the given point

*F*

_{ }, called

**of parabola, and the given straight line, not going through this point**

*a focus*
and called
**
a directrix
**
of parabola.

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

*
y
*
^{
2
}
= 2
*
p
x
*
.

The axis
*
ну
*
is
here an axis of symmetry of parabola.

Let
*
п
*
(
*
У
*
_{
1
}
,
*
С
*
_{
1
}
) be a point of parabola, then
**
an equation of tangent line to
parabola
**
in
this
point
is
:

*
С
*
_{
1
}
*
y
*
^{
}
*
*
=
*
p
*
*
*
(
*
x
*
+
*
У
*
_{
1
}
*
*
) .
*
*

**
A tangency condition of a
straight line
**

*y*=

*m*

*x*+

*k*

*and a parabola**y*

^{ 2 }= 2

*p x*:

*
*
2
*
m k
*
^{
}
=
*
p
*
.