Math 213 - Quadric Surfaces

Quadratic Curves

Cylinders

Quadric Surfaces

Summary

Math 213 - Quadric Surfaces

Peter A. Perry

University of Kentucky

September 11, 2019

Peter A. Perry Math 213 - Quadric Surfaces

University of Kentucky

Quadratic Curves

Reminders

Cylinders

Quadric Surfaces

Summary

? Access your WebWork account only through Canvas!

? Homework A3 on section 12.5 is due tonight ? Homework A4 on section 12.6 is due Friday ? Quiz # 2 on sections 12.3-12.4 takes place in tomorrow's

recitation

Peter A. Perry Math 213 - Quadric Surfaces

University of Kentucky

Quadratic Curves

Cylinders

Quadric Surfaces

Unit I: Geometry and Motion in Space

Summary

12.1 Lecture 1: Three-Dimensional Coordinate Systems 12.2 Lecture 2: Vectors in the Plane and in Space 12.3 Lecture 3:The Dot Product 12.4 Lecture 4:The Cross Product 12.5 Lecture 5: Equations of Lines and Planes, I 12.5 Lecture 6: Equations of Lines and Planes, II 12.6 Lecture 7: Surfaces in Space 13.1 Lecture 8: Vector Functions and Space Curves 13.2 Lecture 9 Derivatives and Integrals of Vector Functions

Lecture 10: Exam I Review

Peter A. Perry Math 213 - Quadric Surfaces

University of Kentucky

Quadratic Curves

Cylinders

Learning Goals

Quadric Surfaces

Summary

? Recall quadratic curves from MA 114 ? Identify and graph cylinders ? Find traces of quadric surfaces ? Identify and graph quadric surfaces

Peter A. Perry Math 213 - Quadric Surfaces

University of Kentucky

Quadratic Curves

y

y

y

Cylinders

Quadric Surfaces

Summary

A quadratic curve is the graph of a second-degree equation

x

in two variables taking one of the forms

Ax2 + By2 + J = 0, Ax2 + By2 + Jy = 0

In MA 114 you learned about the following quadratic curves:

x

?

x2 The ellipse a2

+

y2 b2

= 1 with foci (?c, 0), where

a2 = b2 + c2

? The parabola x2 = 4py with focus at (0, p) and directrix at y = -p

?

x2 The hyperbola a2

-

y2 b2

= 1 with foci at (?c, 0)

x

where c2 = a2 + b2

Peter A. Perry Math 213 - Quadric Surfaces

University of Kentucky

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