Systems: Identifying Equations, Points of Intersections of Equations

Slides:



Advertisements
Similar presentations
Parabolas $ $300 $300 $ $ $ $ $ $ $ $ $ $ $ $ $ $100.
Advertisements

Intro to Conic Sections. It all depends on how you slice it! Start with a cone:
Lesson 10-1 Algebra Check Skills You’ll Need
Circles and Parabolas Review
Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10,
ACT Opener: Find 2
Introduction to Parabolas SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
What is the standard form of a parabola who has a focus of ( 1,5) and a directrix of y=11.
Review Day! Hyperbolas, Parabolas, and Conics. What conic is represented by this definition: The set of all points in a plane such that the difference.
Sullivan Algebra and Trigonometry: Section 11.5 Objectives of this Section Identify a Conic Use a Rotation of Axes to Transform Equations Discuss an Equation.
Circles Ellipse Parabolas Hyperbolas
Circles – An Introduction SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
Conic Sections Conic sections come from the double cones above and a plane that intersects one or both cones, the cross-section provided is then one of.
Algebra Conic Section Review. Review Conic Section 1. Why is this section called conic section? 2. Review equation of each conic section A summary of.
Chapter 8: Test Your Proficiency 8-2 Parabolas 8-3 Circles 8-4 Ellipses 8-5 Hyperbolas 8-6 Identifying Conic Sections Directions: Select a section to work.
QUESTION Identify the following conic section: AB CD CircleParabola EllipseHyperbola.
Section 8.5. In fact, all of the equations can be converted into one standard equation.
8.1 Classifying Conics Section 5/1/2013. Conic Is the intersection of a plane and a right circular cone. Circle Ellipse Parabola Hyperbola Definition:
An Introduction to Conics
Conics Review Study Hard!. Name the Conic without graphing and write it in standard form X 2 + Y 2 -4Y-12=0.
Conics This presentation was written by Rebecca Hoffman.
MATH 1330 Section 8.2A. Circles & Conic Sections To form a conic section, we’ll take this double cone and slice it with a plane. When we do this, we’ll.
Find the distance between (-4, 2) and (6, -3). Find the midpoint of the segment connecting (3, -2) and (4, 5).
Unit 5: Conics Feb. 3, What is Conics? This is the short term for conic sections. -Conic Sections include circles, parabolas, ellipses, and hyperbolas.
Section 15.2 A Brief Catalogue of the Quadratic Surfaces; Projections
Chapter Nonlinear Systems.
9.4 Solving Quadratic Systems Precalculus Precalculus HWQ 3/21/13 Find the standard form of the equation of the hyperbola with vertices ( 2,3) and.
EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.
Chapter 10 – Conic Sections 1) Circles 2) Parabolas 3) Ellipses 4) Hyperbolas.
10.1 Identifying the Conics. Ex 1) Graph xy = 4 Solve for y: Make a table: xy ½ ½ Doesn’t touch y -axis Doesn’t touch x -axis.
Today’s Date: 2/26/ Identifying the Conic Section.
Conic Sections Practice. Find the equation of the conic section using the given information.
10.0 Conic Sections. Conic Section – a curve formed by the intersection of a plane and a double cone. By changing the plane, you can create a circle,
Conics Name the vertex and the distance from the vertex to the focus of the equation (y+4) 2 = -16(x-1) Question:
Chapter 10 Conic Sections.
Chapter 10 Conic Sections
33. Conic Sections in General Form
Systems: Identifying Equations, Points of Intersections of Equations
Solving Quadratic Systems Distance and Midpoint Formula
Solving Systems Graphically
Translating Conic Sections
Warm Up Solve by substitution. Solve by elimination. 3x + 4y = 15 1.
Points of Intersection
MATH 1330 Section 8.2.
Conic Sections Dr. Shildneck Fall, 2015.
Solving Nonlinear Systems
Systems: Identifying Equations, Points of Intersections of Equations
Review Circles: 1. Find the center and radius of the circle.
Conic Sections - Circles
Parabolas Mystery Circles & Ellipses Hyperbolas What am I? $100 $100
10 Topics in Analytic Geometry.
Solving Systems of Linear and Quadratic Equations
CONIC SECTIONS Quadratic Relations Parabola Circle Ellipse Hyperbola.
Systems: Identifying Equations, Points of Intersections of Equations
Test Dates Thursday, January 4 Chapter 6 Team Test
Introduction to Conics: Parabolas
Solving Nonlinear Systems of Equations
Warm-Up Solve the system by graphing..
Solving Systems of Linear and Quadratic Equations
Algebra 2: Conic Sections
Systems: Identifying Equations, Points of Intersections of Equations
MATH 1310 Section 2.8.
MATH 1310 Section 2.8.
MATH 1310 Section 2.8.
Warmup Write the equation in standard form. State whether the graph of 3y2 – 18y – 11 = –x is a parabola, circle, ellipse, or hyperbola. A. x2 + (y – 3)2.
10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.
MATH 1310 Section 2.8.
Jeopardy Solving for y Q $100 Q $100 Q $100 Q $100 Q $100 Q $200
10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.
L10-2 Obj: Students will be able to find equations for parabolas
Presentation transcript:

Systems: Identifying Equations, Points of Intersections of Equations MATH 1330 Systems: Identifying Equations, Points of Intersections of Equations

Classifications of Second Degree Equations

Sometimes equations that look like they should be conic sections do not behave very well. For example,

These are all examples of degenerate conic sections These are all examples of degenerate conic sections. You will not see these very often, but you should be aware of them.

Systems of Second Degree Equations When we graph two conic sections or a conic section and a line on the same coordinate planes, their graphs may contain points of intersection. The graph below shows a hyperbola and a line and contains two points of intersection.

Solving Systems We want to be able to find the points of intersection. To do this, we will solve a system of equations, but now one or both of the equations will be second degree equations. Determining the points of intersection graphically is difficult, so we will do these algebraically.

Popper 18: (a) Parabola (b) Ellipse (c) Circle (d) Hyperbola (e) Degenerate Section or No Graph 2. 1. 3. 4. 5. 6. 7. 8.

Be Sure to Check your Answers!!

Popper 18: Question 9 1 2 3 4

Popper 18: Question 10 a) 10 , 3 b) − 10 ,− 3 c) ± 10 ,± 3 d) ± 10 , 3 e) No Point of Intersection