E
q
u
a
t
i
o
n
Equation
Eq
u
a
t
i
o
n
G
r
a
p
h
Graph
G
r
a
p
h
C
e
n
t
r
e
Centre
C
e
n
t
re
R
a
d
i
u
s
Radius
R
a
d
i
u
s
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
(
0
,
0
)
(0,0)
(
0
,
0
)
a
a
a
(
x
−
h
)
2
+
(
y
−
k
)
2
=
a
2
(x-h)^2+(y-k)^2=a^2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
a
2
(
h
,
k
)
(h,k)
(
h
,
k
)
a
a
a
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2+y^2+2gx+2fy+c=0
x
2
+
y
2
+
2
gx
+
2
f
y
+
c
=
0
(
−
g
,
−
f
)
(-g,-f)
(
−
g
,
−
f
)
g
2
+
f
2
−
c
\sqrt{g^2+f^2-c}
g
2
+
f
2
−
c
Equations of Tangent of all Circles
E
q
u
a
t
i
o
n
s
o
f
Equations\space of
Eq
u
a
t
i
o
n
s
o
f
C
i
r
c
l
e
Circle
C
i
rc
l
e
P
o
i
n
t
/
L
i
n
e
o
f
c
o
n
t
a
c
t
o
f
Point/Line\space of\space contact\space of \space
P
o
in
t
/
L
in
e
o
f
co
n
t
a
c
t
o
f
c
i
r
c
l
e
circle
c
i
rc
l
e
m
=
s
l
o
p
e
o
f
t
a
n
g
e
n
t
\ m=slope \space of \space tangent
m
=
s
l
o
p
e
o
f
t
an
g
e
n
t
E
q
u
a
t
i
o
n
o
f
Equation\space of\space
Eq
u
a
t
i
o
n
o
f
t
a
n
g
e
n
t
tangent
t
an
g
e
n
t
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
(
x
1
,
y
1
)
(x1,y1)
(
x
1
,
y
1
)
x
x
1
+
y
y
1
=
a
2
xx1 +yy1=a^2
xx
1
+
yy
1
=
a
2
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
(
a
c
o
s
θ
,
b
s
i
n
θ
)
(a \space cos\theta,b \space sin\theta)
(
a
cos
θ
,
b
s
in
θ
)
x
c
o
s
θ
+
y
s
i
n
θ
=
a
x \space cos\theta + y \space sin\theta=a
x
cos
θ
+
y
s
in
θ
=
a
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
y
=
m
x
+
c
y=mx+c
y
=
m
x
+
c
y
=
m
x
±
a
1
+
m
2
y=mx±a\sqrt{1+m^2}
y
=
m
x
±
a
1
+
m
2
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2+y^2+2gx+2fy+c=0
x
2
+
y
2
+
2
gx
+
2
f
y
+
c
=
0
(
x
1
,
y
1
)
(x1,y1)
(
x
1
,
y
1
)
x
x
1
+
y
y
1
+
g
(
x
+
x
1
)
+
f
(
y
+
y
1
)
+
c
=
0
xx1+yy1+g(x+x1)+f(y+y1)+c=0
xx
1
+
yy
1
+
g
(
x
+
x
1
)
+
f
(
y
+
y
1
)
+
c
=
0
Equations of Normal of all Circles
E
q
u
a
t
i
o
n
s
o
f
Equations\space of
Eq
u
a
t
i
o
n
s
o
f
C
i
r
c
l
e
Circle
C
i
rc
l
e
P
o
i
n
t
/
L
i
n
e
o
f
c
o
n
t
a
c
t
o
f
Point/Line\space of\space contact\space of \space
P
o
in
t
/
L
in
e
o
f
co
n
t
a
c
t
o
f
c
i
r
c
l
e
circle
c
i
rc
l
e
m
=
s
l
o
p
e
o
f
t
a
n
g
e
n
t
\ m=slope\space of \space tangent
m
=
s
l
o
p
e
o
f
t
an
g
e
n
t
E
q
u
a
t
i
o
n
o
f
Equation\space of\space
Eq
u
a
t
i
o
n
o
f
N
o
r
m
a
l
\ Normal
N
or
ma
l
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
(
x
1
,
y
1
)
(x1,y1)
(
x
1
,
y
1
)
x
x
1
=
y
y
1
\frac{x}{x1}=\frac{y}{y1}
x
1
x
=
y
1
y
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
(
a
c
o
s
θ
,
b
s
i
n
θ
)
(a \space cos\theta,b \space sin\theta)
(
a
cos
θ
,
b
s
in
θ
)
y
=
x
t
a
n
θ
y=x\space tan\theta
y
=
x
t
an
θ
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
y
=
m
x
+
c
y=mx+c
y
=
m
x
+
c
x
+
m
y
=
±
a
1
+
m
2
x+my=±a\sqrt{1+m^2}
x
+
m
y
=
±
a
1
+
m
2
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2+y^2+2gx+2fy+c=0
x
2
+
y
2
+
2
gx
+
2
f
y
+
c
=
0
(
x
1
,
y
1
)
(x1,y1)
(
x
1
,
y
1
)
y
−
y
1
x
−
x
1
=
y
1
+
f
x
1
+
g
\frac{y-y1}{x-x1}=\frac{y1+f}{x1+g}
x
−
x
1
y
−
y
1
=
x
1
+
g
y
1
+
f
Director Circle of all Circles
E
q
u
a
t
i
o
n
s
o
f
C
i
r
c
l
e
Equations\space of\space Circle
Eq
u
a
t
i
o
n
s
o
f
C
i
rc
l
e
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
Eq
u
a
t
i
o
n
o
f
D
i
rec
t
or
C
i
rc
l
e
x
2
+
y
2
=
a
2
x^2+y^2=a^2
x
2
+
y
2
=
a
2
x
2
+
y
2
=
2
a
2
x^2+y^2=2 \space a^2
x
2
+
y
2
=
2
a
2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
a
2
(x-h)^2+(y-k)^2=a^2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
a
2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
2
a
2
(x-h)^2+(y-k)^2=2 \space a^2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
2
a
2
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2+y^2+2gx+2fy+c=0
x
2
+
y
2
+
2
gx
+
2
f
y
+
c
=
0
(
x
+
g
)
2
+
(
y
+
f
)
2
=
2
(
g
2
+
f
2
−
c
)
(x+g)^2+(y+f)^2=2(g^2+f^2-c)
(
x
+
g
)
2
+
(
y
+
f
)
2
=
2
(
g
2
+
f
2
−
c
)
