Unit 6 Conic Sections

University:
University of California, Berkeley
Course:
MATH W54 | Linear Algebra and Differential Equations
Academic year:

2021
Views:

65

Pages:

2
Author:

chondinny0r70

Unit 6 Conic Sections The graphs are abbreviated ‘f’ is focus, ‘v’ is vertex, and ‘d’ is directrix Parabolas are a set of points that are the same distance to a point (focus) and a line (directrix). Model (𝑥 − ℎ)2 = 4𝑎(𝑦 − 𝑘) (𝑦 − ℎ𝑘 = 4𝑎(𝑥 − ℎ) Vertex (ℎ, 𝑘) (ℎ, 𝑘) Focus (ℎ, 𝑘 + 𝑎) (ℎ + 𝑎, 𝑘) Directrix 𝑦=𝑘−𝑎 𝑥 =ℎ−𝑎 (ℎ ± 2𝑎, 𝑘 + 𝑎) (ℎ + 𝑎, 𝑘 ± 2𝑎) Latus Recum (Points) Ellipses are a set of points whose total or sum distance from 2 points (foci) is the same. Model (𝑥−ℎ)2 𝑎2 + (𝑦−𝑘)2 𝑏2 =1 a>b (𝑥−ℎ)2 𝑎2 + (𝑦−𝑘)2 𝑏2 =1 (ℎ, 𝑘) (ℎ, 𝑘) Vertices (ℎ ± 𝑎, 𝑘) (ℎ, 𝑘 ± 𝑏) Covertices (ℎ, 𝑘 ± 𝑏) (ℎ ± 𝑎, 𝑘) Latus Recum (Points) (ℎ ± 𝑐, 𝑘) (ℎ, 𝑘 ± 𝑐) Center a< b A Hyperbola is a set of points whose difference in distance from the 2 foci is the same. Model (𝑥−ℎ)2 𝑎2 − (𝑦−𝑘)2 𝑏2 =1 (𝑦−𝑘) 𝑏2 − (𝑥−ℎ)2 𝑎2 =1 (ℎ, 𝑘) (ℎ, 𝑘) Vertices (ℎ ± 𝑎, 𝑘) (ℎ, 𝑘 ± 𝑏) Foci 𝑐 2 = 𝑎2 + 𝑏 2 (ℎ ± 𝑐, 𝑘) (ℎ, 𝑘 ± 𝑐) 𝑏 𝑦 − 𝑘 = ± (𝑥 − ℎ) 𝑎 𝑏 𝑦 − 𝑘 = ± (𝑥 − ℎ) 𝑎 Center asymptotes