E
q
u
a
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
D
i
r
e
c
t
r
i
x
Directrix
D
i
r
e
c
t
r
i
x
L
e
n
g
t
h
o
f
T
r
a
n
s
v
e
r
s
e
A
x
i
s
Length\space of\space Transverse\space Axis
L
e
n
g
t
h
o
f
T
r
a
n
s
v
e
r
s
e
A
x
i
s
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1
a
2
x
2
−
b
2
y
2
=
1
(
±
a
e
,
0
)
(±ae,0)
(
±
a
e
,
0
)
2
b
2
a
\frac{2b^2}{a}
a
2
b
2
x
=
±
a
e
x=±\frac{a}{e}
x
=
±
e
a
2
a
2a
2
a
y
2
b
2
−
x
2
a
2
=
1
\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1
b
2
y
2
−
a
2
x
2
=
1
(
0
,
±
b
e
)
(0,±be)
(
0
,
±
b
e
)
2
a
2
b
\frac{2a^2}{b}
b
2
a
2
y
=
±
b
e
y=±\frac{b}{e}
y
=
±
e
b
2
b
2b
2
b
x
2
−
y
2
=
a
2
{x^2}\space-{y^2}\space={a^2}
x
2
−
y
2
=
a
2
(
0
,
±
a
2
)
(0, ±a{\sqrt{2}} )
(
0
,
±
a
2
)
2
a
2a
2
a
x
=
±
a
2
x=±\frac{a}{\sqrt{2}}
x
=
±
2
a
2
a
2a
2
a
Equations of Tangent of Hyperbola
E
q
u
a
t
i
o
n
Equation
E
q
u
a
t
i
o
n
P
a
r
a
m
e
t
r
i
c
C
o
o
r
d
i
n
a
t
e
s
Parametric\space Coordinates
P
a
r
a
m
e
t
r
i
c
C
o
o
r
d
i
n
a
t
e
s
E
q
u
a
t
i
o
n
o
f
t
a
n
g
e
n
t
Equation\space of\space tangent
E
q
u
a
t
i
o
n
o
f
t
a
n
g
e
n
t
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
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1
a
2
x
2
−
b
2
y
2
=
1
(
a
s
e
c
θ
,
b
t
a
n
θ
)
(asec\theta,btan\theta)
(
a
s
e
c
θ
,
b
t
a
n
θ
)
y
=
m
x
±
a
m
2
−
b
2
y=mx±\sqrt{am^2-b^2}
y
=
m
x
±
a
m
2
−
b
2
c
=
±
a
m
2
−
b
2
c=±\sqrt{am^2-b^2}
c
=
±
a
m
2
−
b
2
y
2
b
2
−
x
2
a
2
=
1
\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1
b
2
y
2
−
a
2
x
2
=
1
(
b
s
e
c
θ
,
a
t
a
n
θ
)
(bsec\theta,atan\theta)
(
b
s
e
c
θ
,
a
t
a
n
θ
)
y
=
m
x
±
−
b
m
2
+
a
2
y=mx±\sqrt{-bm^2+a^2}
y
=
m
x
±
−
b
m
2
+
a
2
c
=
±
−
b
m
2
+
a
2
c=±\sqrt{-bm^2+a^2}
c
=
±
−
b
m
2
+
a
2
x
2
−
y
2
=
a
2
{x^2}\space-{y^2}\space={a^2}
x
2
−
y
2
=
a
2
(
a
s
e
c
θ
,
a
t
a
n
θ
)
(asec\theta,atan\theta)
(
a
s
e
c
θ
,
a
t
a
n
θ
)
y
=
m
x
±
a
m
2
−
a
2
y=mx±\sqrt{am^2-a^2}
y
=
m
x
±
a
m
2
−
a
2
c
=
±
a
m
2
−
a
2
c=±\sqrt{am^2-a^2}
c
=
±
a
m
2
−
a
2
Equations of Normal of Hyperbola
E
q
u
a
t
i
o
n
Equation
E
q
u
a
t
i
o
n
P
a
r
a
m
e
t
r
i
c
C
o
o
r
d
i
n
a
t
e
s
Parametric\space Coordinates
P
a
r
a
m
e
t
r
i
c
C
o
o
r
d
i
n
a
t
e
s
E
q
u
a
t
i
o
n
o
f
N
o
r
m
a
l
Equation\space of\space Normal
E
q
u
a
t
i
o
n
o
f
N
o
r
m
a
l
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
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1
a
2
x
2
−
b
2
y
2
=
1
(
a
s
e
c
θ
,
b
t
a
n
θ
)
(asec\theta,btan\theta)
(
a
s
e
c
θ
,
b
t
a
n
θ
)
a
x
s
e
c
θ
+
b
y
t
a
n
θ
=
a
2
+
b
2
\frac{ax}{sec\theta}+\frac{by}{tan\theta}=a^2+b^2
s
e
c
θ
a
x
+
t
a
n
θ
b
y
=
a
2
+
b
2
c
=
m
(
a
2
+
b
2
)
a
2
−
b
2
m
2
c=\frac{m(a^2+b^2)}{\sqrt{a^2-b^2m^2}}
c
=
a
2
−
b
2
m
2
m
(
a
2
+
b
2
)
y
2
b
2
−
x
2
a
2
=
1
\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1
b
2
y
2
−
a
2
x
2
=
1
(
b
s
e
c
θ
,
a
t
a
n
θ
)
(bsec\theta,atan\theta)
(
b
s
e
c
θ
,
a
t
a
n
θ
)
b
x
s
e
c
θ
+
a
y
t
a
n
θ
=
b
2
+
a
2
\frac{bx}{sec\theta}+\frac{ay}{tan\theta}=b^2+a^2
s
e
c
θ
b
x
+
t
a
n
θ
a
y
=
b
2
+
a
2
c
=
m
(
b
2
−
a
2
)
a
2
m
2
−
b
2
c=\frac{m(b^2-a^2)}{\sqrt{a^2m^2-b^2}}
c
=
a
2
m
2
−
b
2
m
(
b
2
−
a
2
)
x
2
−
y
2
=
a
2
{x^2}\space-{y^2}\space={a^2}
x
2
−
y
2
=
a
2
(
a
s
e
c
θ
,
a
t
a
n
θ
)
(asec\theta,atan\theta)
(
a
s
e
c
θ
,
a
t
a
n
θ
)
x
s
e
c
θ
+
y
t
a
n
θ
=
2
a
\frac{x}{sec\theta}+\frac{y}{tan\theta}=2a
s
e
c
θ
x
+
t
a
n
θ
y
=
2
a
c
=
2
a
m
1
−
m
2
c=\frac{2am}{\sqrt{1-m^2}}
c
=
1
−
m
2
2
a
m
Equations of Director Circle of Hyperbola
E
q
u
a
t
i
o
n
Equation
E
q
u
a
t
i
o
n
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
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1
a
2
x
2
−
b
2
y
2
=
1
x
2
+
y
2
=
a
2
−
b
2
x^2\,+\,y^2\space\,=a^2\,-\,b^2
x
2
+
y
2
=
a
2
−
b
2
y
2
b
2
−
x
2
a
2
=
1
\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1
b
2
y
2
−
a
2
x
2
=
1
x
2
+
y
2
=
b
2
−
a
2
x^2\,+\,y^2\space\,=b^2\,-\,a^2
x
2
+
y
2
=
b
2
−
a
2
