Dari Wikibuku bahasa Indonesia, sumber buku teks bebas
Vertikal
Horisontal
Titik pusat (0,0)
Persamaan
y
2
a
2
−
x
2
b
2
=
1
{\displaystyle {\frac {y^{2}}{a^{2}}}-{\frac {x^{2}}{b^{2}}}=1}
x
2
a
2
−
y
2
b
2
=
1
{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1}
Sumbu utama
sumbu y (x=0)
sumbu x (y=0)
Panjang sumbu mayor (nyata)
2a
2a
Panjang sumbu minor (khayal, sekawan (konjugat))
2b
2b
Panjang Latus Rectum
L
=
2
b
2
a
{\displaystyle L={\frac {2b^{2}}{a}}}
L
=
2
b
2
a
{\displaystyle L={\frac {2b^{2}}{a}}}
Fokus
F
(
0
,
±
c
)
{\displaystyle F(0,\pm c)}
F
(
±
c
,
0
)
{\displaystyle F(\pm c,0)}
Puncak
P
(
0
,
±
a
)
{\displaystyle P(0,\pm a)}
P
(
±
a
,
0
)
{\displaystyle P(\pm a,0)}
Asimtot
y
=
±
a
b
x
{\displaystyle y=\pm {\frac {a}{b}}x}
y
=
±
b
a
x
{\displaystyle y=\pm {\frac {b}{a}}x}
Direktris
y
=
±
a
2
c
{\displaystyle y=\pm {\frac {a^{2}}{c}}}
x
=
±
a
2
c
{\displaystyle x=\pm {\frac {a^{2}}{c}}}
Eksentrisitas
e
=
c
a
{\displaystyle e={\frac {c}{a}}}
e
=
c
a
{\displaystyle e={\frac {c}{a}}}
Titik pusat (h,k)
Persamaan
(
y
−
k
)
2
a
2
−
(
x
−
h
)
2
b
2
=
1
{\displaystyle {\frac {(y-k)^{2}}{a^{2}}}-{\frac {(x-h)^{2}}{b^{2}}}=1}
(
x
−
h
)
2
a
2
−
(
y
−
k
)
2
b
2
=
1
{\displaystyle {\frac {(x-h)^{2}}{a^{2}}}-{\frac {(y-k)^{2}}{b^{2}}}=1}
Sumbu utama
x = h
y = k
Panjang sumbu mayor (nyata)
2a
2a
Panjang sumbu minor (khayal, sekawan (konjugat))
2b
2b
Panjang Latus Rectum
L
=
2
b
2
a
{\displaystyle L={\frac {2b^{2}}{a}}}
L
=
2
b
2
a
{\displaystyle L={\frac {2b^{2}}{a}}}
Fokus
F
(
h
,
k
±
c
)
{\displaystyle F(h,k\pm c)}
F
(
h
±
c
,
k
)
{\displaystyle F(h\pm c,k)}
Puncak
P
(
h
,
k
±
a
)
{\displaystyle P(h,k\pm a)}
P
(
h
±
a
,
k
)
{\displaystyle P(h\pm a,k)}
Asimtot
(
y
−
k
)
=
±
a
b
(
x
−
h
)
{\displaystyle (y-k)=\pm {\frac {a}{b}}(x-h)}
(
y
−
k
)
=
±
b
a
(
x
−
h
)
{\displaystyle (y-k)=\pm {\frac {b}{a}}(x-h)}
Direktris
y
=
k
±
a
2
c
{\displaystyle y=k\pm {\frac {a^{2}}{c}}}
x
=
h
±
a
2
c
{\displaystyle x=h\pm {\frac {a^{2}}{c}}}
Eksentrisitas
e
=
c
a
{\displaystyle e={\frac {c}{a}}}
e
=
c
a
{\displaystyle e={\frac {c}{a}}}
dimana
c
=
a
2
+
b
2
{\displaystyle c={\sqrt {a^{2}+b^{2}}}}
bergradien
m
{\displaystyle m}
y
=
m
x
+
c
{\displaystyle y=mx+c}
Vertikal
Horisontal
Titik pusat (0,0)
y
=
m
x
±
a
2
−
b
2
m
2
{\displaystyle y=mx\pm {\sqrt {a^{2}-b^{2}m^{2}}}}
y
=
m
x
±
a
2
m
2
−
b
2
{\displaystyle y=mx\pm {\sqrt {a^{2}m^{2}-b^{2}}}}
Titik pusat (h,k)
y
−
k
=
m
(
x
−
h
)
±
a
2
−
b
2
m
2
{\displaystyle y-k=m(x-h)\pm {\sqrt {a^{2}-b^{2}m^{2}}}}
y
−
k
=
m
(
x
−
h
)
±
a
2
m
2
−
b
2
{\displaystyle y-k=m(x-h)\pm {\sqrt {a^{2}m^{2}-b^{2}}}}
jika persamaan garis lurus bergradien sejajar maka
m
2
=
m
1
{\displaystyle m_{2}=m_{1}}
jika persamaan garis lurus bergradien tegak lurus maka
m
2
=
−
1
m
1
{\displaystyle m_{2}={\frac {-1}{m_{1}}}}
melalui titik
(
x
1
,
y
1
)
{\displaystyle (x_{1},y_{1})}
dengan cara bagi adil
Vertikal
Horisontal
Titik pusat (0,0)
y
y
1
a
2
−
x
x
1
b
2
=
1
{\displaystyle {\frac {yy_{1}}{a^{2}}}-{\frac {xx_{1}}{b^{2}}}=1}
x
x
1
a
2
−
y
y
1
b
2
=
1
{\displaystyle {\frac {xx_{1}}{a^{2}}}-{\frac {yy_{1}}{b^{2}}}=1}
Titik pusat (h,k)
(
y
−
k
)
(
y
1
−
k
)
a
2
−
(
x
−
h
)
(
x
1
−
h
)
b
2
=
1
{\displaystyle {\frac {(y-k)(y_{1}-k)}{a^{2}}}-{\frac {(x-h)(x_{1}-h)}{b^{2}}}=1}
(
x
−
h
)
(
x
1
−
h
)
a
2
−
(
y
−
k
)
(
y
1
−
k
)
b
2
=
1
{\displaystyle {\frac {(x-h)(x_{1}-h)}{a^{2}}}-{\frac {(y-k)(y_{1}-k)}{b^{2}}}=1}
jika titik
(
x
1
,
y
1
)
{\displaystyle (x_{1},y_{1})}
jika titik
(
x
1
,
y
1
)
{\displaystyle (x_{1},y_{1})}
