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 a focus
of parabola, and the given straight line, not going through this point
and called a directrix
of parabola.
An equation of parabola
( Fig.1
) is :
y^{ 2} = 2
p
x
.
The axis
ÎÕ
is
here an axis of symmetry of parabola.
Let Ð
( õ_{1}
, ó_{
1}
) be a point of parabola, then an equation of tangent line to
parabola in
this
point
is
:
ó_{
1}
y^{ }
=
p
(
x
+
õ_{1}
) .
A tangency condition of a
straight line y
= m
x
+ k and a parabola y^{
2} = 2
p
x
:
2
m k^{
}
=
p .
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