11
Precalculus
pre
Quarter 1 – Module 1
ANALYTIC GEOMETRY
i
,Pre-calculus – Grade 11
Alternative Delivery Mode
Quarter 1 – Module 1: Analytic Geometry
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any
work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for
exploitation of such work for profit. Such agency or office may, among other things,
impose as a condition the payment of royalty.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand
names, trademarks, etc.) included in this book are owned by their respective
copyright holders. Every effort has been exerted to locate and seek permission to
use these materials from their respective copyright owners. The publisher and
authors do not represent nor claim ownership over them.
Published by the Department of Education – Division of Cagayan de Oro
Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V
Development Team of the Module
Author/s: Mar V. Agot Alex M. Acedera
Reviewers: Jean S. Macasero, EPS Science
Illustrator and Layout Artist:
Management Team
Chairperson: Cherry Mae L. Limbaco, PhD, CESO V
Schools Division Superintendent
Co-Chairperson: Alicia E. Anghay, PhD, CESE
Assistant Schools Division Superintendent
Members
Lorebina C. Carrasco, OIC-CID Chief
Jean S. Macasero, EPS Science
Joel D. Potane, LRMS Manager
Lanie O. Signo, Librarian II
Gemma Pajayon, PDO II
Printed in the Philippines by
Department of Education – Division of Cagayan de Oro City
Office Address: Fr. William F. Masterson Ave Upper Balulang Cagayan de Oro
Telefax: (08822)855-0048
E-mail Address:
ii
, Precalculus
MODULE 1:
Analytic Geometry
This instructional material was collaboratively developed and reviewed
by educators from public and private schools, colleges, and/or universities.
We encourage teachers and other education stakeholders to email their
feedback, comments, and recommendations to the Department of Education
at .
We value your feedback and recommendations.
Department of Education • Republic of the Philippines
iii
, Table of Contents
What This Module is About 1
What I need to know 2
How to learn from this Module 3
Icons of this Module 3
What I Know (Pretest) 4
Lesson 1 – Introduction of Conic Sections and the Circle
What I Need to Know 9
What’s In 9
What’s New 10
What Is It 11
What’s More 18
What I Have Learned 22
What I Can Do 23
Lesson 2 – The Parabola
What I Need to Know 28
What’s In 28
What’s New 29
What Is It 30
What’s More 37
What I Have Learned 42
What I Can Do 42
Lesson 3 – The Ellipse
What I Need to Know 45
What’s In 45
What’s New 47
What Is It 47
What’s More 54
What I Have Learned 59
What I Can Do 60
Lesson 4 – The Hyperbola
What I need to Know 61
What’s In 61
What’s New 63
What Is It 64
What’s More 72
What I Have Learned 72
What I Can Do 73
Lesson 5 – Equation and Important Characteristics of Different
Types of Conic Sections
What I need to Know 75
What’s In 75
What’s New 77
What Is It 78
What’s More 79
iv
Precalculus
pre
Quarter 1 – Module 1
ANALYTIC GEOMETRY
i
,Pre-calculus – Grade 11
Alternative Delivery Mode
Quarter 1 – Module 1: Analytic Geometry
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any
work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for
exploitation of such work for profit. Such agency or office may, among other things,
impose as a condition the payment of royalty.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand
names, trademarks, etc.) included in this book are owned by their respective
copyright holders. Every effort has been exerted to locate and seek permission to
use these materials from their respective copyright owners. The publisher and
authors do not represent nor claim ownership over them.
Published by the Department of Education – Division of Cagayan de Oro
Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V
Development Team of the Module
Author/s: Mar V. Agot Alex M. Acedera
Reviewers: Jean S. Macasero, EPS Science
Illustrator and Layout Artist:
Management Team
Chairperson: Cherry Mae L. Limbaco, PhD, CESO V
Schools Division Superintendent
Co-Chairperson: Alicia E. Anghay, PhD, CESE
Assistant Schools Division Superintendent
Members
Lorebina C. Carrasco, OIC-CID Chief
Jean S. Macasero, EPS Science
Joel D. Potane, LRMS Manager
Lanie O. Signo, Librarian II
Gemma Pajayon, PDO II
Printed in the Philippines by
Department of Education – Division of Cagayan de Oro City
Office Address: Fr. William F. Masterson Ave Upper Balulang Cagayan de Oro
Telefax: (08822)855-0048
E-mail Address:
ii
, Precalculus
MODULE 1:
Analytic Geometry
This instructional material was collaboratively developed and reviewed
by educators from public and private schools, colleges, and/or universities.
We encourage teachers and other education stakeholders to email their
feedback, comments, and recommendations to the Department of Education
at .
We value your feedback and recommendations.
Department of Education • Republic of the Philippines
iii
, Table of Contents
What This Module is About 1
What I need to know 2
How to learn from this Module 3
Icons of this Module 3
What I Know (Pretest) 4
Lesson 1 – Introduction of Conic Sections and the Circle
What I Need to Know 9
What’s In 9
What’s New 10
What Is It 11
What’s More 18
What I Have Learned 22
What I Can Do 23
Lesson 2 – The Parabola
What I Need to Know 28
What’s In 28
What’s New 29
What Is It 30
What’s More 37
What I Have Learned 42
What I Can Do 42
Lesson 3 – The Ellipse
What I Need to Know 45
What’s In 45
What’s New 47
What Is It 47
What’s More 54
What I Have Learned 59
What I Can Do 60
Lesson 4 – The Hyperbola
What I need to Know 61
What’s In 61
What’s New 63
What Is It 64
What’s More 72
What I Have Learned 72
What I Can Do 73
Lesson 5 – Equation and Important Characteristics of Different
Types of Conic Sections
What I need to Know 75
What’s In 75
What’s New 77
What Is It 78
What’s More 79
iv
