PARABOLA
ENTER DATA
Coefficient of
x
², a
¹
0
a:
Coefficient of
x
b:
Constant =
y
-intercept
c:
x
1
:
(
x
2
>
x
1
)
x
2
:
Parabola as entered
[
Critical Points
]
[
Roots
]
Vertex moved to (0,0)
[
Focus-Directrix Data
]
[
Tangent at (
x
2,
y
2)
]
[
Normal at (
x
2,
y
2)
]
Region of Parabola:
[
to
x
-axis
]
[
to Line through (
x
2,
y
2)
]
[
Chord (
x
1,
y
1)-(
x
2,
y
2)
]
PARABOLA DATA
y
= a(
x
- p)
^{ 2}
+ q
Vertex at (p,q)
[
INDEX
] [
ENTER DATA
]
x
1
:
y
1
:
x
2
:
y
2
:
a =
Axis of Symmetry
p =
q =
y
-intercept =
Roots
[
INDEX
] [
ENTER DATA
]
+
i
+
i
Equivalent parabola:
y
= a
x
^{ 2}
Vertex at (0,0)
[
INDEX
] [
ENTER DATA
]
x
1
:
y
1
:
x
2
:
y
2
:
Focus-Directrix Data
r = k
¸
(1 - sin θ)
Origin at Focus
[
INDEX
] [
ENTER DATA
]
Directrix =
Focus =
Focus to Directrix
k =
Focus to (
x
2,
y
2)
r =
Angle to
x
-axis
θ =
Tangent at (
x
2
,
y
2
)
[
INDEX
] [
ENTER DATA
]
Slope =
*
Angle to
x
-axis =
x
-intercept =
y
-intercept =
*
Equals the value of Parametric angle φ at
specified (
x
,
y
) for calculation of Arc length
Normal at (
x
2
,
y
2
)
[
INDEX
] [
ENTER DATA
]
Slope =
Angle to
x
-axis =
x
-intercept =
y
-intercept =
Parabola to
x
-axis
Vertical Elements
Scope: First Quadrant, 0
£
x
1
£
x
2
[
INDEX
] [
ENTER DATA
]
A =
A
x-axis
=
ý
=
A
y-axis
=
x
=
I
x-axis
=
I
y-axis
=
Neutral axis || to
x
-axis
I =
Neutral axis || to
y
-axis
I =
Parabola to Line through (
x
2
,
y
2
)
Vertical Elements
Scope: First Quadrant, 0
£
x
1
£
x
2
[
INDEX
] [
ENTER DATA
]
A =
A
x-axis
=
ý
=
A
y-axis
=
x
=
I
x-axis
=
I
y-axis
=
Neutral axis || to
x
-axis
I =
Neutral axis || to
y
-axis
I =
Parabola bounded by Chord
Vertical Elements
Scope: First Quadrant, 0
£
x
1
£
x
2
[
INDEX
] [
ENTER DATA
]
A =
A
x-axis
=
ý
=
A
y-axis
=
x
=
I
x-axis
=
I
y-axis
=
Neutral axis || to
x
-axis
I =
Neutral axis || to
y
-axis
I =
Arc Length =
Chord =
Secant Slope =
Secant θ to
x
-axis =
Secant
y
-intercept =
[
INDEX
] [
ENTER DATA
]
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