What is an open Interval?
(a,b):={x : a<x<b}.
What is a closed Interval
What is a half opened half closed interval?
(a,b]:={x : a<x≤b}
what is a circles parametric equation?
(x,y) = (a+rcosθ,b+rsinθ).
what is the general equation for a conic section
L/(1+ecos(theta))
where L is a positive constant and e is the eccentricity
What is the equation of an ellipse
(x/a)^2 + (y/b)^2 = 1
the parametric version is
(x,y) = (acosθ,bsinθ)
What is the equation of a parabola?
y^2 = 4ax
with parametric equation
(x, y) = (at2, 2at)
What is the standard equation for a hyperbola?
(x/a)^2 + (y/b)^2 = 1
with parametric equation
(x,y) = (±acoshθ,bsinhθ)
what are the equations for polar coordinates?
x = rcos(theta)
y = rsin(theta)