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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