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Level 511

Circles, Ellipses, Parabolas & Hyperbolas


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[pi]r^2
Area of a circle
2[pi]r
Center of a circle
y=a(x-h)^2+k
standard form of a vertical parabola
Y=
Parabola Axis of Symmetry
Y=
Parabola Focus
Y=
Parabola Directrix
|1/a|
Parabola LR
Y=
Parabola Direction of Opening
**a>b**
Ellipse Forms
E=c/a
Ellipse/Hyperbola Eccentricity
B^2+c^2=a^2
Ellipse Random Formula
(h,k)
Center of a ellipse
Ellipse V maj. A
(Form is x/a)
(Form is x/b)
Ellipse V maj. B
(Form is x/a)
Ellipse V min. A
=2a
Ellipse L maj./Hyperbola LT
=2b
Ellipse L min./Hyperbola LC
Ellipse Focus A
(Form is x/a)
Ellipse Focus B
(Form is x/b)
[pi]ab
Ellipse Area
2[pi]{sq.rt. of a^2+b^2/2}
Ellipse (how to find c)
2b^2/a
LR (Hyperbola)
Circle form
(X-h)^2 + (Y-k)^2 = r^2
Hyperbola forms
**a is first, but not necessarily larger
Hyperbola Random Formula
A^2 + B^2 = C^2
Hyperbola Vertex
(Form is x/a)
Hyperbola Focus
(Form is x/a)
Hyperbola MA X
(Form is x/a)
Hyperbola MA Y
(Form is y/a)
Ellipse (locus def)
collection of points such that the sum of the distance from 2 fixed points it constant
a (ellipse)
half of major axis (always bigger than b)
Major Axis
The longer axis on an ellipse with vertices
Minor Axis
The shorter axis on an ellipse with co vertices
b (ellipse)
half of minor axis
c (ellipse)
distance from center to either focus
a^2-b^2=c^2
How to find foci/c (ellipse)
vertices (ellipse)
Endpoints of the major axis
semi ellipse equation (0,0)
y=+/-n/m square root: m^2-x^2 (m=x denominator, n=y denominator)
ellipse equation (center at 0,0)
x^2/m^2 + y^2/n^2 = 1
ellipse equation (center at h,k)
(x-h)^2/m^2 + (y-k)^2/n^2 = 1
Hyperbola
Equation subtracts x²/a and y²/b=1; x and y coefficients have different signs.
hyperbola equation (0,0)
x^2/m^2 - y^2/n^2 = 1
x term is subtracted
if the transverse is vertical
if transverse is horizontal
y term is subtracted
Vertices (hyperbola )
endpoints of the transversal axis
transverse
line with endpoints at the vertices
semi ellipse equation (h,k)
y = k +/- n/m square root m^2 - (x-h)^2
Asymptote
An imaginary line on a graph that acts as a boundary line.
a (hyperbola)
the front term's denominator
b (hyperbola)
the last term's denominator
c (hyperbola)
distance from center to foci
Parabola
the graph of a quadratic function
Circle
r= asin(theta)
Ellipse
Equation adds x²/a² and y²/b²=1
y=ax (squared)
parabola opens up or down. a>0 opens up. a<0 opens down
x=ay (squared)
parabola opens left or right. a>0 opens right. a<0 opens left.
lal=1/4c
c=distance
circle distance formula
(x-h)^2 + (x-k)^2 = r^2
(h,k)
center of a circle
radius
From center to a point on the circle.
a>0
the parabola opens upward if
vertex
The point where two sides meet. (Shared end points of the line segments of a polygon.)
covertex
vertex on longer side
opposite of an ellipse
foci of a hyperbola