Review: Standard equations of conic sections with vertex (vertices at the origin - x=0 and y = 0)
 

I. Parabola         The parabola is the set of all points (x, y) that are equidistant from a          fixed line (directrix) and a fixed point (focus) not on the line.         (a) Standard equation with vertex (0, 0) and directrix y = -p               (vertical axis): x2 = 4py         (b) Standard equation with vertex (0, 0) and directrix x = -p              (horizontal axis): y2 = 4px         (c) The focus lies on the axis p units (directed distance) from the vertex.

II. Ellipse         An ellipse is the set of all points (x,y) the sum of whose distances from              two distinct fixed points (foci) is constant.         (a) Standard equation of an ellipse with center (0,0), major axis                length 2a, and minor axis length 2b:         1. Horizontal major axis:          2. Vertical major axis:          (b) The foci lie on the major axis, c units from the center, where a, b,                and c are related by the equation c2 = a2 - b2 .         (c) The vertices and endpoints of the minor axis are:         1. Horizontal axis: (a, 0) and (0, b) 2. Vertical axis: (0, (a) and ((b, 0)

III. Hyperbola         A hyperbola is the set of all points (x, y) the difference of whose distances from two distanct fixed points (foci) is constant.         (a) Standard equation of hyperbola with center (0,0):         1. Horizontal transverse axis:          2. Vertical transverse axis:          (b) The vertices and foci are a and c units from the center and b2 = c2 - a2 .         (c) The asymtotes of the hyperbola are:         1. Horizontal transverse axis: y =          1. Vertical transverse axis: y =

Section 11-II  Conics with center (h, k)