E
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u
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t
i
o
n
Equation
E
q
u
a
t
i
o
n
G
r
a
p
h
Graph
G
r
a
p
h
F
o
c
u
s
Focus
F
o
c
u
s
L
e
n
g
t
h
o
f
L
R
Length\space of\space LR
L
e
n
g
t
h
o
f
L
R
E
q
u
a
t
i
o
n
o
f
D
i
r
e
c
t
r
i
x
Equation\space of\space Directrix
E
q
u
a
t
i
o
n
o
f
D
i
r
e
c
t
r
i
x
E
q
u
a
t
i
o
n
o
f
A
x
i
s
Equation\space of\space Axis
E
q
u
a
t
i
o
n
o
f
A
x
i
s
y
2
=
4
a
x
y^2=4ax
y
2
=
4
a
x
(
a
,
0
)
(a,0)
(
a
,
0
)
4
a
4a
4
a
x
=
−
a
x=-a
x
=
−
a
y
=
0
y=0
y
=
0
y
2
=
−
4
a
x
y^2=-4ax
y
2
=
−
4
a
x
(
−
a
,
0
)
(-a,0)
(
−
a
,
0
)
4
a
4a
4
a
x
=
a
x=a
x
=
a
y
=
0
y=0
y
=
0
x
2
=
4
a
y
x^2=4ay
x
2
=
4
a
y
(
0
,
a
)
(0,a)
(
0
,
a
)
4
a
4a
4
a
y
=
−
a
y=-a
y
=
−
a
x
=
0
x=0
x
=
0
x
2
=
−
4
a
y
x^2=-4ay
x
2
=
−
4
a
y
(
0
,
−
a
)
(0,-a)
(
0
,
−
a
)
4
a
4a
4
a
y
=
a
y=a
y
=
a
x
=
0
x=0
x
=
0
Equations of Tangent of all Parabolas in slope form
E
q
u
a
t
i
o
n
s
o
f
Equations\space of
E
q
u
a
t
i
o
n
s
o
f
P
a
r
a
b
o
l
a
Parabola
P
a
r
a
b
o
l
a
P
o
i
n
t
o
f
c
o
n
t
a
c
t
i
n
Point\space of\space contact\space in
P
o
i
n
t
o
f
c
o
n
t
a
c
t
i
n
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
\space terms\space of\space slope(m)
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
E
q
u
a
t
i
o
n
o
f
t
a
n
g
e
n
t
i
n
Equation\space of\space tangent\space in
E
q
u
a
t
i
o
n
o
f
t
a
n
g
e
n
t
i
n
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
\space terms\space of\space slope(m)
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
C
o
n
d
i
t
i
o
n
o
f
T
a
n
g
e
n
c
y
Condition\space of\space Tangency
C
o
n
d
i
t
i
o
n
o
f
T
a
n
g
e
n
c
y
y
2
=
4
a
x
y^2=4ax
y
2
=
4
a
x
(
a
m
2
,
2
a
m
)
(\frac{a}{m^2},\frac{2a}{m})
(
m
2
a
,
m
2
a
)
y
=
m
x
+
a
m
y=mx+\frac{a}{m}
y
=
m
x
+
m
a
c
=
a
m
c=\frac{a}{m}
c
=
m
a
y
2
=
−
4
a
x
y^2=-4ax
y
2
=
−
4
a
x
(
−
a
m
2
,
−
2
a
m
)
(-\frac{a}{m^2},-\frac{2a}{m})
(
−
m
2
a
,
−
m
2
a
)
y
=
m
x
−
a
m
y=mx-\frac{a}{m}
y
=
m
x
−
m
a
c
=
−
a
m
c=-\frac{a}{m}
c
=
−
m
a
x
2
=
4
a
y
x^2=4ay
x
2
=
4
a
y
(
2
a
m
,
a
m
2
)
(2am,am^2)
(
2
a
m
,
a
m
2
)
y
=
m
x
−
a
m
2
y=mx-am^2
y
=
m
x
−
a
m
2
c
=
−
a
m
2
c=-am^2
c
=
−
a
m
2
x
2
=
−
4
a
y
x^2=-4ay
x
2
=
−
4
a
y
(
−
2
a
m
,
a
m
2
)
(-2am,am^2)
(
−
2
a
m
,
a
m
2
)
y
=
m
x
+
a
m
2
y=mx+am^2
y
=
m
x
+
a
m
2
c
=
a
m
2
c=am^2
c
=
a
m
2
Equations of Normal of all Parabolas in slope form
E
q
u
a
t
i
o
n
s
o
f
Equations\space of
E
q
u
a
t
i
o
n
s
o
f
P
a
r
a
b
o
l
a
Parabola
P
a
r
a
b
o
l
a
P
o
i
n
t
o
f
c
o
n
t
a
c
t
i
n
Point\space of\space contact\space in
P
o
i
n
t
o
f
c
o
n
t
a
c
t
i
n
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
\space terms\space of\space slope(m)
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
E
q
u
a
t
i
o
n
o
f
n
o
r
m
a
l
i
n
Equation\space of\space normal\space in
E
q
u
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t
i
o
n
o
f
n
o
r
m
a
l
i
n
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
\space terms\space of\space slope(m)
t
e
r
m
s
o
f
s
l
o
p
e
(
m
)
C
o
n
d
i
t
i
o
n
o
f
N
o
r
m
a
l
i
t
y
Condition\space of\space Normality
C
o
n
d
i
t
i
o
n
o
f
N
o
r
m
a
l
i
t
y
y
2
=
4
a
x
y^2=4ax
y
2
=
4
a
x
(
a
m
2
,
−
2
a
m
)
(am^2,-2am)
(
a
m
2
,
−
2
a
m
)
y
=
m
x
−
2
a
m
−
a
m
3
y=mx-2am-am^3
y
=
m
x
−
2
a
m
−
a
m
3
c
=
−
2
a
m
−
a
m
3
c=-2am-am^3
c
=
−
2
a
m
−
a
m
3
y
2
=
−
4
a
x
y^2=-4ax
y
2
=
−
4
a
x
(
a
m
2
,
2
a
m
)
(am^2,2am)
(
a
m
2
,
2
a
m
)
y
=
m
x
+
2
a
m
+
a
m
3
y=mx+2am+am^3
y
=
m
x
+
2
a
m
+
a
m
3
c
=
2
a
m
+
a
m
3
c=2am+am^3
c
=
2
a
m
+
a
m
3
x
2
=
4
a
y
x^2=4ay
x
2
=
4
a
y
(
−
2
a
m
,
a
m
2
)
(-\frac{2a}{m},\frac{a}{m^2})
(
−
m
2
a
,
m
2
a
)
y
=
m
x
+
2
a
+
a
m
2
y=mx+2a+\frac{a}{m^2}
y
=
m
x
+
2
a
+
m
2
a
c
=
2
a
+
a
m
2
c=2a+\frac{a}{m^2}
c
=
2
a
+
m
2
a
x
2
=
−
4
a
y
x^2=-4ay
x
2
=
−
4
a
y
(
2
a
m
,
−
a
m
2
)
(\frac{2a}{m},-\frac{a}{m^2})
(
m
2
a
,
−
m
2
a
)
y
=
m
x
−
2
a
−
a
m
2
y=mx-2a-\frac{a}{m^2}
y
=
m
x
−
2
a
−
m
2
a
c
=
−
2
a
−
a
m
2
c=-2a-\frac{a}{m^2}
c
=
−
2
a
−
m
2
a
Director Circle of all Parabolas
E
q
u
a
t
i
o
n
s
o
f
P
a
r
a
b
o
l
a
Equations\space of\space Parabola
E
q
u
a
t
i
o
n
s
o
f
P
a
r
a
b
o
l
a
E
q
u
a
t
i
o
n
o
f
D
i
r
e
c
t
o
r
C
i
r
c
l
e
Equation\space of\space Director\space Circle
E
q
u
a
t
i
o
n
o
f
D
i
r
e
c
t
o
r
C
i
r
c
l
e
y
2
=
4
a
x
y^2=4ax
y
2
=
4
a
x
x
+
a
=
0
x\,+a\space=\,0
x
+
a
=
0
y
2
=
−
4
a
x
y^2=-4ax
y
2
=
−
4
a
x
x
−
a
=
0
x\,-a\space=\,0
x
−
a
=
0
x
2
=
4
a
y
x^2=4ay
x
2
=
4
a
y
y
+
a
=
0
y\,+a\space=\,0
y
+
a
=
0
x
2
=
−
4
a
y
x^2=-4ay
x
2
=
−
4
a
y
y
−
a
=
0
y\,-a\space=\,0
y
−
a
=
0
