Question

ろぐちゃん

放物線についての質問です。黒い丸で囲んだところがなぜ成り立つのかを教えて欲しいです。

9585b2f1981a9b1fc6895fb92a57852f.png 808x8957
Conic:
Equation:
Equation
(Horizontal)
Graph
(Horizontal)
Equation
(Vertical)
Graph
(Vertical)
Circle
Center: (h, k)
(x-h)²-(y-k)² = r
Same
Same
To get r:
Additional
Information y==√√²-(x-h)² + k
Parabola
Vertex: (h, k)
x= a(y-k)² +h
or
x-h=a(y-k)²
or
b(x-h)=(y-k)²
(Positive Coefficient)
D: x=
V
P P
F
y=a(x-h)² +k
or
y-k=a(x-h)²
V
2p
or
b(y-k)=(x-h)²
(Positive Coefficient)
2p
D: y=
For x-h=a(y-k):
1
1
a=
p=40 4p
For b(x-h)=(y-k)²:
b
b=4p; P=4
p=focal length
Negative Coefficients:
Flip parabola
https://i.pinimg.com/originals/95/85/b2/9585b2f1981a9b1fc6895fb92a57852f.png
Ellipse
Center: (h, k)
a always larger than b
今までの2次関数と同じ!
y=2x² →x²=54
?P=&
(x-h)²(y-k)²
+(x-k)²
Horizontal: Focus (P/O)
#
y²4ex, XFP
Vertral: focus (P₁0)
(y=+x²) x²= Apy youp is directrix
b²
Co-V
Co-V
b
C
Co-V
(x-h)²+(-k)=1
(x−h)²_(y-k)²
a²
C
a
directrix,
a
X
V
b
=1
c²=a²-b²
F
Co-V
Hyperbola
Center: (h, k)
a always before the "-"
(x-h)²_(y-k)²
a²
(Diago) Asymptotes:
Ty=-p
8/21/22 午後 5:24
q²
y-k=±=(x-h)
Co-V
b²
Co-V
-=1
a
Co-V
(y-k)²_(x-h)²
6²
Asymptotes:
y-k=±(x-h)
=1
c²=a² +6²
Co-V
1/1ページ

放物線