GRADE 1 to 12
DAILY LESSON LOG
Angel M. Del Rosario High
School
Teacher Mrs. Judy Ann M. Danan
School
Teaching Date and Time
Session 1
Grade Level
Learning Area
11
Pre-Calculus
Session 2
Quarter
Session 3
The learner demonstrates
understanding of key concepts of conic
sections and systems of nonlinear
equations
The learner demonstrates
understanding of key concepts of conic
sections and systems of nonlinear
equations
The learner demonstrates
understanding of key concepts of conic
sections and systems of nonlinear
equations
The learner shall be able to model
situations appropriately and solve
problems accurately using conic
sections and systems of nonlinear
equations.
Learning Competency:
Defines a parabola. STEM_PC11AG-Ia-5
Learning Objectives:
1. Define a parabola
2. Determine the properties of
parabola
3. Show appreciation to the
concept about parabola
The learner shall be able to model
situations appropriately and solve
problems accurately using conic
sections and systems of nonlinear
equations.
determine the standard form of
equation of a parabola
(STEM_PC11AG-Ib-1)
The learner shall be able to model
situations appropriately and solve
problems accurately using conic
sections and systems of nonlinear
equations.
determine the standard form of
equation of a parabola
(STEM_PC11AG-Ib-1)
STANDARD FORM OF A PARABOLA
STANDARD FORM OF A PARABOLA
September 11-15, 2023
First
Session 4
I. OBJECTIVES
A.
B.
Content Standard
The learner demonstrates
understanding of key concepts of conic
sections and systems of nonlinear
equations
Performance Standard
The learner shall be able to model
situations appropriately and solve
problems accurately using conic
sections and systems of nonlinear
equations.
C. Learning Competency/Objectives
Write the LC code for each.
II.
Learning Competency:
Defines a circle. STEM_PC11AG-Ia-2
Determines the standard form of
equation of a circle. STEM_PC11AG-Ia3
Graphs a circle in a rectangular
coordinate system STEM_PC11AG-Ia-4
Learning Objectives:
1. Convert standard form to general
form of equation of circle and vice
versa
2. Solve problems involving circle
3. Demonstrate appreciation to the
concept about circles
CONTENT
CIRCLES
PARABOLA
III. LEARNING RESOURCES
A.
References
1. Teacher’s Guide pages
2.
Learner’s Materials pages
1
3.
Textbook pages
4.
B.
Additional Materials from
Learning Resource
(LR)portal
Other Learning Resource
IV. PROCEDURES
A.
B.
Reviewing previous lesson or
presenting the new lesson
ACTIVITY 1
In this activity, the teacher will call
students to give their answers orally.
Direction: Given the standard equation
of the circle , identify the center and
radius of the circle
1. (x-2)2+(y+1)2=9
2. (x+3)2+y2=9
2
2
3. (x+2) +(y-1) =3
ACTIVITY 1
In this activity, the students will work in
pairs.
Direction: In Grade 9 Mathematics,
parabola is the graph of quadratic
functions. To refresh your idea about
parabola, do the task below.
1. Given the quadratic functions,
determine the concavity and vertex.
a. y=x2-4
b. y=(x-2)2 + 3
c. y=2
(x+1)
d. y=-x2-3
Establishing a purpose for the
lesson
The teacher presents the objectives of
the lesson to the class and let the
students recognize the importance of
the concept of circles
C. Presenting examples/Instances of
the new lesson
ACTIVITY 2
In this activity, the students will work in
pairs.
Direction: To determine the equation
of the circle given the graph, locate the
center first and determine the distance
from the center to any point on the
circle to determine the radius. Do the
task below. The teacher goes around
the room to provide needed support.
Given the graphs of the circles, give the
standard equation of the circle.
The teacher presents the objectives of
the lesson to the class and let the
students recognize the importance of
the concept of parabola
ACTIVITY 2
In this activity, the students will work
with the same partner.
Direction: Shown in the figure below is
a parabola. Do the task below. The
teacher goes around the room to
provide needed support.
Let the distance from a point on the
parabola to the point in parabola be
equal to the distance from the same
point on the parabola to line outside
the parabola.
Recap:
1. What is the definition of a
parabola?
2. How are the concepts of focus
and directrix used to define a
parabola?
The teacher lets the students realize
that one’s knowledge in parabolas is
very important since its shape and
characteristics are widely used in
practical applications such as the
design of parabolic mirrors,
searchlights, and automobile
headlights; the path of a projectile
motion; arches and cables of a
suspension bridge; and dish antennas.
Show pictures of the different
applications of parabola.
The teacher will ask questions to
review the previous lesson:
1. What are the different
standard forms of the
equation of a parabola when
the vertex is at the origin?
2. What are the properties of
parabolas at V (0,0)?
The teacher lets the students realize
that one’s knowledge in parabolas is
very important since its shape and
characteristics are widely used in
practical applications such as the
design of parabolic mirrors,
searchlights, and automobile
headlights; the path of a projectile
motion; arches and cables of a
suspension bridge; and dish antennas.
2
1. Determine the distance of the
following:
a. A to D
b. C to D
c. B to D
d. E to D
2. Distance from the broken line to the
following points.
a. A
b. B
C. C
D. D
e. E
D. Discussing new concepts and
practicing new skills # 1

The teacher talks about the concept
about general form of the equation of
the circle. The teacher will relate the
Activity a1 and 2 to the topic about
circles. In addition, he/she presents
some sample problems involving circles
with solutions
E.
Discussing new concepts and
practicing new skills # 2
The teacher talks about the concept
parabola. The teacher will relate the
Activity 1 and 2 to the topic about
parabola. Furthermore, he/she
describe the properties of parabola.
The teacher will discuss and
illustrate thoroughly the derivation
of the standard form of the
equation of a parabola.

The teacher will ask the
students to examine the figures
and generalize the features of the
graph of a parabola with standard
equation x2=4cy or x2=-4cy,
where c>0. Ensure that all
concepts presented below are
included:
 Vertex: origin V (0,0)
 Directrix: the line y = -c or
y=c
 Focus: F (0,c) or F (0, -c)
 Axis of Symmetry: x = 0
(the y-axis)
 Latus Rectum:
+4c2, c & -4c2, c or +4c2, -c & -4c2,- c
In groups of 4, the teacher will let the
students discover the equations and
features of parabolas with horizontal
axes by examining the figure below:
The teacher will discuss and illustrate
thoroughly the equation and properties
of a parabola whose vertex is not at the
origin { V (h,k) } presented on page 2324 of the Learner’s Module.
In groups of 5, let the students go over
Examples 1.2.3 – 1.2.5 to illustrate and
practice solving for the properties of a
parabola at V (h,k) found on page 24-26
3
of the Learner’s Module..

F.
Developing mastery
(leads to Formative Assessment
3)
ACTIVITY 3
In this activity, the students will work
with the same partner.
Direction: The standard equation of the
circle describes the center and radius of
the circle, do the task below. The
teacher goes around providing needed
support.
1. Given the standard equation of the
circle transform them to general form.
a. (x-2)2 + (y+3)2=16
b. (x+5)2+ y2 = 9
2. Given the general equation of the
circle transform them to standard form.
a. x2+y2-2x+8y+4=0
b. x2+y2-6x-2y-5=0
ACTIVITY 3
In this activity, the students will work
with the same partner.
Direction: Do the task below. The
teacher goes around the room to
provide needed support.
1. Determine whether the following
equations describe a parabola or not.
a. x2-4x+4-y=0 b. x-y2-2x+3=0 c.
x2+y2-2x+4y-1=0
d. 4x2-2y+6x3y+1=0
2. Determine the opening of the
following equations of parabola.
a. y=2x2
b. x=-3y2-1
c.
x=4(y-2)2-3
d.y =-3(x+1)2
Standard Equation:
y2=4cx or y2=-4cx
 Vertex: origin V (0,0)
 Directrix: the line x = -c or
x=c
 Focus: F (c,0) or F (-c,0)
 Axis of Symmetry: y = 0
(the x-axis)
 Latus Rectum:
c,+4c2 & c,-4c2 or -c,+4c2 & -c,-4c2
From the given equation and graph;
find the focus, equation of the directrix,
vertex, axis of symmetry, and the
endpoints of the latus rectum by pair.
1. x2=12y
2.
Depending on the pace of the students
and their level of readiness, the teacher
may provide more exercises (#’s 3, 4, &
6) found on page 29-30 of the Learner’s
Module.
y2=7x
4
G. Finding practical application of
concepts and skills in daily living
H. Making generalizations and
abstractions about the lesson
ACTIVITY 4
In this activity, the students will work
with the same partner.
Direction: Do the task below. The
teacher goes around providing needed
support.
1. A street with two lanes, each of 10 ft.
wide, goes through a semi-circular
tunnel with radius 12ft. How high is the
tunnel at the edge of each lane? Round
off to 2 decimal places.
Answer Key: 6.63 ft.
The teacher summarizes the
mathematical concept of circles.
Moreover, he/she gives in dealing with
problems involving circles.
Formulate 5 equations in standard
form of a parabola with Vertex at the
origin and the focus at (a , 0) and (0 , a),
where a is any integer except 0. This
will be done by group.
The teacher summarizes the
mathematical concept of parabola.
Likewise, he/she gives examples to
some applications of parabola.
Let the students generalize the
equations of a parabola and their
corresponding features:
 An equation of the parabola
having its focus at (0 , c) and
having as its directrix the line y
= -c is x2=4cy and line y = c is
x2=-4cy.
An equation of the parabola having its
focus at (c , 0) and having as its
directrix the line x = -c is y2=4cx and
line x = c is y2=-4cx.
Let the students generalize the
equations of a parabola at V (h,k) when
the directrix is horizontal and vertical.
5
I.
Evaluating learning
Direction: Do the task given.
1. Given the equation below, sketch its
graph and indicate the center and
radius.
a. x2+y2+8y=0
b. x2+y24x+2y=0
2. A circular play area with radius of 3m
is to be partitioned into two sections
using a straight fence as shown in the
figure below. How long should be the
fence?
Direction: Do the task given.
1. Given the figure below, determine
the distance of the following:
I.
For the parabola having the
equation, find (a) the vertex, (b)
the axis, (c) the focus, and (d) an
equation of the directrix, and (e)
the endpoints of the latus rectum.
1. x = 4y
2. x = -16y
3. y = 12x
4. y = -8x
Find an equation of the
parabola
having
the
given
properties:
II.
1. Focus, (0,4); directrix, y = -4
2. Focus, (2,0); directrix, x = -2
2
2
2
2
II.
a. A to D
b. B to D
c. C to D
2. Give an equation of parabola for the
following description
a. facing down b. opening to the left
c. facing to the right d. opening up
3. What is a parabola?
I.
For the parabola having the
equation, find (a) the vertex, (b) an
equation of the the axis, (c) the
focus, and (d) an equation of the
directrix, and (e) the endpoints of
the latus rectum.
1. y = x – 4
2. y = -x + 4x – 5
3. x = y – 6y
4. x – 6x – 4y + 13 = 0
5. y + 4x + 12y = 0
A parabola has focus F (-2,-5)
and directrix x = 6. Find the
standard equation of the parabola.
2
2
2
2
2
6
J.
Additional activities for application
or remediation
V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80% in
the evaluation
B. No. of learners who require
additional activities for remediation who
scored below 80%
C. Did the remedial lessons work? No.
of learners who have caught up with
the lesson
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these work?
F. What difficulties did I encounter
which my principal or supervisor can
help me solve?
G. What innovation or localized
materials did I use/discover which I
wish to share with other teachers?
Prepared by:
JUDY ANN M. DANAN
Teacher I
Inspected by:
ELIZABETH R. MAWAL
Head Teacher III
Noted:
ELISEO C. DELA CRUZ
Secondary School Principal I
7