Conic Sections Flashcards
1
Q
What is an open Interval?
A
(a,b):={x : a<x<b}.
2
Q
What is a closed Interval
A
3
Q
What is a half opened half closed interval?
A
(a,b]:={x : a<x≤b}
4
Q
what is a circles parametric equation?
A
(x,y) = (a+rcosθ,b+rsinθ).
5
Q
what is the general equation for a conic section
A
L/(1+ecos(theta))
where L is a positive constant and e is the eccentricity
6
Q
What is the equation of an ellipse
A
(x/a)^2 + (y/b)^2 = 1
the parametric version is
(x,y) = (acosθ,bsinθ)
7
Q
What is the equation of a parabola?
A
y^2 = 4ax
with parametric equation
(x, y) = (at2, 2at)
8
Q
What is the standard equation for a hyperbola?
A
(x/a)^2 + (y/b)^2 = 1
with parametric equation
(x,y) = (±acoshθ,bsinhθ)
9
Q
what are the equations for polar coordinates?
A
x = rcos(theta)
y = rsin(theta)
10
Q
A
