Saturday, May 19, 2007

Recap of Conics

In light of the test on monday, I'm taking it upon myself to recap some important values and other stuff for conics
Ellipses:
Vertex=the point where the major axis and the ellipse intersect
a=length of the semimajor axis (half the larger axis)=vertex-center
b=length of the semiminor axis (half the shorter axis)
c=distance from focus to center, c^2=a^2-b^2
The foci are always on the semimajor axis
general equation:
(x-h)^2/a^2+(y-k)^2/b^2=1 for horizotnal major axis
(y-k)^2/a^2+(x-h)^2/b^2=1 for vertical major axis

Parabolas:
Vertex= the point at the bottom of the parabola (top if the parabola is upside down), x-coord of the vertex=-b/2a if ax^2+bx+c=0
p: for an equation like this: (x-h)^2=a(y-k), a=4p, p represents the distance from the vertex to the focus or directrix

Hyperbolas:
a=distance from the center to the vertex of one curve of the hyperbola
b: the equation of the asymptote is (y-k)=b/a(x-h)
c: distance from the center to either focus, c^2=a^2+b^2 (remember, plus in hyperbolas, minus in ellipses)
genral formula:
(x-h)^2/a^2-(y-k)^2/b^2=1 for hyperbolas with horizontal axes,
(y-k)^2/a^2-(x-h)^2/b^2=1 for vertical hyperbolas

If you want to add anything, please do! I want to know what I've forgotten.

-Kevin

1 Comments:

Blogger MannyLau said...

thanks this helps a lot, do we need to know how to covert these equations to parametric equations?

7:39 PM  

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