University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2024
Views:

63

Pages:

2
Author:

CometConductor

HPC Ellipses ELLIPSES Name: Horizontal Ellipse Vertical Ellipse Graph Equation x  h2   y  k 2 a2 b2 1 x  h2   y  k 2 b2 a2 1 Major Axis Minor Axis Vertices Co-Vertices Foci Eccentricity EXAMPLE 1 – Graphing a Translated Ellipse Put the equation in standard form, then identify the vertices, co-vertices, and foci of the ellipse. Lastly, graph the ellipse. 9𝑥 2 + 16𝑦 2 − 18𝑥 + 64𝑦 − 71 = 0 Center: Vertices: Co-Vertices: Foci: EXAMPLE 2 – Writing Equations Find the standard form of the equation of each ellipse a. b. c. Foci: (0, ± 2) Vertices: (0, ± 4) d. Foci: (± 7, 0) Length of Major Axis: 20 e. Major axis vertical with length 20 Length of minor axis 10; Center (2, −3) f. Endpoints of major axis: (2, 2) & (8, 2) Endpoints of minor axis: (5, 3) & (5, 1)