MATH 26
CHAPTER 1
Analytic Geometry
and the Conic
Sections
Mathematics Division
Institute of Mathematical Sciences and Physics
College of Arts and Sciences
U. P. Los Baos
1
Chapter
Objectives chapter, you should be
Upon completion of this
able to:
find
e
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
1.5 Ellipse
1
Q
Non-degenerate
Conic
e
P
Q2
Given the eccentricity
of a conic section, the
conic is
P2
parabola if e = 1;
P1
Q1
ellipse if 0 < e < 1;
focus
vertex
directrix
F
hyperbola if e > 1.
principal axis
2
El
MATH 26
CHAPTER 1
Analytic Geometry
and the Conic
Sections
Mathematics Division
Institute of Mathematical Sciences and Physics
College of Arts and Sciences
U. P. Los Baos
1
Chapter
Objectives chapter, you should be
Upon completion of this
able to:
find
e
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
1.3
Conic
Sections
1
Conic Sections
2
Conic Sections
Flashlight Conic Sections:
The light emitted from a
flashlight with a circular
lens is projected as a
cone from the light bulb.
You can create Flashlight
Conic
S
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
1
1.6 Hyperbola
Non-degenerate Conic
Q
P
Q2
Given the eccentricity e
of a conic section, the
conic is
P2
parabola if e = 1;
P1
Q1
ellipse if 0 < e < 1;
focus
vertex
directrix
F
hyperbola if e > 1.
principal axis
2
1.7 General second
degree equations
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
GENERAL SECOND
DEGREE EQUATIONS
A general second-degree equation in x and y
is of the form
Ax Bxy Cy Dx Ey F 0
2
2
where A, B, C, D, E and F are constants and
in which not all of
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
1.2
Analytic Proof
1
2
1.2 Analytic Proof
Objectives: Upon completion of this section,
you should be able to:
use Cartesian coordinate system to label
parts of some known geometric figures,
use Cartesian coordina
I.
POINT OF VIEW
This paper took the point of view of the finance manager of the Agri-Tech Company. The
officers of the company task the finance manager to manage all operations on whether they
will accept Dr. Melgars proposal of producing and marketing R
Chapter 7: Organizing
Organizing dividing work and coordinating divided work
process of identifying activities needed to accomplish a goal,
subdividing and grouping these activities into meaningful
units, and assigning authority and responsibility to peop
1.4 Parabola
MATH 26
ANALYTIC GEOMETRY
AND CALCULUS I
1.4 Parabola
Objectives: At the end of this section
students should be able to:
give the standard equation of a
parabola;
identify parts of a parabola;
sketch the graph of a parabola.
Non-degenerate Co
Planning Seminar
*Ateneo Goals Form
*Activities List
*General Budget Proposal
Group Dynamics (whenever it gets boring)
Open Forum (+ inuman after or at night)
Vision and Mission of the Organization
Objectives
Focus for the Year
Constitution
Roles & System
REPUBLIC ACT NO. 8049
AN ACT REGULATING HAZING AND OTHER
FORM OF INITIATION RITES IN FRATERNITIES,
SORORITIES, AND ORGANIZATIONS AND
PROVIDING PENALTIES THEREFORE
Be it enacted by the Senate and House of Representative
of the Philippines in Congress Assem
II. THE PRODUCT.
The business concept statement is "E-F Jeepney for cleaner environment
Our service is e-jeepney. It runs on electricity and it is also eco-friendly because it emits
less pollution. Our costumers is students, faculty members, professors an
Group 1
Olfindo, Hannah Marikit, I. (2015-65638)
Kalaw, Rene Jose M. (2015-65529)
Montevirgen, Madeleine DL. (2015-65621)
Marty, Guila Mariz V. (2015-65598)
Binay, Eduard Kevin dG. (2015-65015)
Case Study:Mountain West Health Plan
I. Point of View
Mr. Qui
Madeleine DL. Montevirgen
MGT 101 - T
Reaction Paper
"People dont but buy what you do, they buy why you do it" Simon Sinek's message is
both edgy and wise. This is for all people who wants to inspire and lead others.
Simon explains the Golden Circle which
Group 1
Olfindo, Hannah Marikit, I. (2015-65638)
Kalaw, Rene Jose M. (2015-65529)
Montevirgen, Madeleine DL. (2015-65621)
Marty, Guila Mariz V. (2015-65598)
Binay, Eduard Kevin dG. (2015-65015)
Case Study:Mountain West Health Plan
I. Point of View
Mr Quin
Olfindo, Hannah Marikit I. (2015-65638)
Kalaw, Rene Jose M. (2015-65529)
Montevirgen, Madeleine DL. (2015-65621)
Marty, Guila Mariz V. (2015-65598)
Binay, Eduard Kevin dG. (2015-65015)
CASE STUDY: Lincoln Electric
I.
Point of View
In this case, we choose
Lecture 2: Astronomy
Early agrarian society made observations of the movement of the stars and planets across the sky.
First astronomers:
Egyptians (Belt of Orion)
Arabs (Navigation)
Mesopotamians (Devices)
Chinese (Detect positioning of celestial bodies)
Yngeez
Science is Mans attempt to make the chaotic diversity
of his sense experience correspond to a logically
uniform system of thought. Albert Einstein
3.
History
Prior to 15th century: methods of analysis of
nature
o Religious methods
Universe is crea
Baral, Kathrina
Brazal, Brian
Delos Reyes, Lester
Gesmundo, Allen Gerald
Pereira, Gamiello
Tolentino, Rosmund Lemuel
Agri-Tech Product Company Case Analysis
I.
Point of View
The Agri-Tech Product Company case will be analyzed from the financial
consultant