Lesson Plan for Mathematics Grade 11
(Ellipse)
School
Subjects
Grade
Semester
Time Allocation
: Laboratory School, Tarlac Agricultural University
: Mathematics
: 11 (Senior High School)
:1
: 1 meeting (120 minutes)
Learning Competency :
a. The learner determines conic section by the given equation.
b. The leraner are able to solve problem involving conic section.
I.
Objectives
At the end of the lesson, the students should have been able to:
a. Define an Ellipse
b. Determine the standard form of equation of an ellipse
c. Sketch the graph of an ellipse
II.
Subject Matter
a. Title: Conic Section
b. Materials: Power Point Presentation, laptop, LCD projector, board, chalk,
broad, eraser
III.
Procedure/Lesson Proper
Activities
A. Preliminary
Activities
1. Routine
2. Review
B. Motivation
Check the attendance, cleanliness of the classroom and
proper seating arrangement of the students
Ask the students:
a. Determine the graph of the following equation.
b. What is the focus in a parabola?
Tell the students about ellipse in real life. Example: The
paths of the planets and comets as they move about the
sun.
C. Lesson Proper
1. Presentation/ac Present the lesson of the day: determine the definition of
tivities
ellipse, the parts of ellipse, the equation of ellipse, and
sketch the graph.
2. Discussion and The definition of an ellipse.
Ellipse is a geometric figure which is defined as a set of
analysis
points whose sum of the distance from the 2 fixed points,
the foci is always constant and is equal to 2𝑎.
Parts of an ellipse.
a. Foci, fixed two points of an ellipse.
b. Major axis, a line segment through the foci extending
between (a, 0) and (-a, 0) or between (0, a) and (0, -a).
c. Semimajor axis, the length a.
d. Minor axis, a segment of the other line of symmetry
between (b, 0) and (-b, 0) or (0, b) and (0, -b).
e. Semiminor axis, the length b.
f. Vertices, two points in the end of the major axis.
g. Sub-vertices, two points in the en of the minor axis.
Area of an ellipse.
𝐴 = 𝜋𝑎𝑏
A : Area of an ellipse
a : Distance between the center to vertices.
b : Distance between the center to sub-vertices
Standard form of the equation of an ellipse.
a. Horizontal Ellipse
(𝑥 − ℎ)
(𝑦 − 𝑘)
+
=1
𝑎
𝑏
b. Vertical Ellipse
(𝑥 − ℎ)
(𝑦 − 𝑘)
+
=1
𝑏
𝑎
NOTE :
 (h, k) as the coordinate of the center of the ellipse
 𝑎 =𝑏 +𝑐
General equation of a parabola
𝑎𝑥 + 𝑏𝑦 + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0
Give some example
Determine the equation of an ellipse by the following :
1. Center at the origin, sub-vertex at (3, 0), and vertex at
(0, -5)
2. Center at the origin, focus at (0, 3), and vertex at (0, -4)
3. Find the equation of an ellipse, if two of the vertices of
an ellipse have coordinates A (0, -3), B (0, 3), and the
distance between foci an ellipse is 8.
Find the center, vertices, foci, and sub-vertices of the
following ellipse
1.
+ =1
2. 9𝑥 + 16𝑦 − 36𝑥 − 32𝑦 − 102 = 0
Sketch the graph of an ellipse
1. Identifying the parts of the ellipse
2. Sketch the graph
3. Fixing skills
and guided
practice and
application
4. Generalization
IV.
Give an example
Sketch the graph of 81𝑥 + 1681𝑦 + 486𝑥 − 16810𝑦 −
93407 = 0
1. Find the center, vertices, foci, and sub-vertices of each
ellipse
a.
+𝑦 =1
b. 16𝑥 + 9𝑦 = 144
c. 5𝑥 + 9𝑦 − 45 = 0
2. Find the equation of each ellipse
a. Foci at (3, 0) and (-3, 0), vertices at (4, 0) and (-4,
0)
b. Foci at (0, 2) and (0, -2), major axis 8
c. Minor axis 5, vertices at (7, 0) and (-7, 0)
What is the difference between circle and ellipse? Do
ellipse have a directrix?
Evaluation
Teacher will evaluate the students based on the following knowledge/skill:
a. Determining the foci, vertices, sub-vertices, center, minor axis, and major axis
of an ellipse.
b. Determining the equation of an ellipse by the given information.
c. Sketch the graph of an ellipse.
Teacher will evaluate the students from the assignment and the test that will be
held in the end of the meeting.
V.
Assignment or Agreement
1. Find the equation of an ellipse, if two of the vertices of an ellipse have
coordinates A (0, -3), B (0, 3), and the distance between foci an ellipse is 4.
2. The area of an ellipse is 88 . Find the equation of an ellipse if the distance
between the 2 vertices is 14 and the center of the ellipse is at the origin.
3. Sketch the graph of the following ellipse :
a. 4𝑥 + 9𝑦 + 16𝑥 − 18𝑦 − 11 = 0
b. 2𝑥 + 3𝑦 − 8𝑥 + 6𝑦 + 5 = 0