Conic Sections Review

Parabolas:

The basic equations for a parabola are (x-h)^2 = 4p(y-k) and (y-k)^2 = 4p(x-h).

P is the distance between the vertex and its focus, which is in the same direction as the parabola, and between the vertex and the directrix, or a line directly behind the parabola. (h,k) are the rectangular coordinates for the vertex.

Ellipses:

The basic equations for ellipses are:

[(y-k)^2]/a^2 + [(x-h)^2]/b^2              AND          [(x-h)^2]/a^2 + [(y-k)^2]/b^2       (h,k) are the rectangular coordinates of the ellipse's center. a is half of the major axis (longer "diameter") and b is half of the minor axis (shorter "diameter"). Hyperbolas:  Once again, (h,k) are the coordinates of the center. A and b are the distances from the center to the edge of a rectangle through which the asymptotes of the graph pass diagonally. A will also be the distance from the center to the vertices of the hyperbola