ENGL 10600 Lecture Notes - Lecture 35: Ellipse, Hyperbola

• School: Purdue University
• Department: English
• Course: ENGL 10600
• Professor: Crumrie

Document Summary

Parabola = all points equidistant from a line called the directrix and a point called the focus. For a vertical parabola with vertex at the origin, it has an equation x^2=4py, where the focus is at point (0,p) and the equation of the directrix is y=(-p) Flip x and y for a horizontal one. Has equation (x^2)/(a^2) + (y^2)/(b^2) = 1. X intercept = +/- a, y intercept = +/- b. Major axis is length from center to vertices, minor axis is length from center to co-vertices. Foci are located on major axis at (+/- c, 0); c^2 = a^2 - b^2 (assuming a is larger) If ellipse is vertical instead of horizontal, a (the larger value) will be under y instead of x. Hyperbola = all points the difference of whose distance from two fixed points (foci) is constant; two parabolas mirrored on the same axis. Has equation (x^2)/(z^2) - (y^2)/(b^2) = 1.