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Parabola Definition

Set of all points in a plane that are equidistant from a particular point to a particular line

Parabola equation

x^2=4py

focal width

4p

P

the distance from the vertex to the focus

Ellipse Definition

Set of all points in a plane whose distances from two fixed points (the foci) have a constant sum

Ellipse pythag

a^2=b^2+c^2

Ellipse 'a' placement

always largest and under the dominant term

Hyperbola defintion

set of all points in a plane whose distances from two fixed points have a common difference

Ellipse equation

x^2/a^2 + y^2/b^2=1

Hyperbola Equation

x^2/a^2 -y^2/b^2

Hyperbola 'a' placement

is fixed. direction is determined by x or y term first

Hyperbola pythag

c^2=a^2+b^2

Hyperbola Discriminant

B^2-4AC>0

Parabola Discriminant

B^2-4AC=0

Ellipse discriminant

B^2-4AC<0