Republic of the Philippines
Department of Education
Region I
SCHOOLS DIVISION OFFICE I PANGASINAN
Urbiztondo District
Detailed Lesson Plan in Mathematics 10
I. LEARNING OBJECTIVES
The learners will be able to:
a. Illustrates the center-radius form of the equation of a circle.
b. Write the equation of a circle in center – radius form (standard form) given the
center and radius of a circle
c. Write the equation of a circle form to general form and vice versa.
d. Sketch the graph an Illustrate how to find the center and the radius of the
equation of a circle
e. Find the center and the radius of the equation of a circle.
II. CONTENT AND MATERIALS
Topic:
Equation of a Circle
Textbook: Mathematics 10 Learner’s Module pp. 252-269
Reference: Mathematics 10 Teacher’s Guide pp.221 - 229
Materials: laptop, TV Monitor, chalk and chalkboard
III. TEACHING - LEARNING PROCEDURE
TEACHER’S ACTIVITY
A. Preliminaries
Good afternoon class!
Before we start, everybody stand up
and let us pray.
(Checking of attendance)
Who are absent today?
Very Good!
Now bring out your assignment.
B. Lesson Proper
What was our topic last meeting?
Very good!
What is the formula in finding the
distance between two points? the
midpoint formula?
Very good!
STUDENTS' ACTIVITY
Good afternoon Ma’am!
None Ma’am!
Distance and midpoint formula
Ma’am.
C. Presentation and Development of the
Lesson
I have here our topic for today. But
Circle – set of all points
before that what is a circle?
equidistant from a given point
called the center of the circle.
Wow…perfect!
So we can name the circle by its
center which is in point c.
Therefore, the name of the circle is
circle c.
Can you name some other parts of
a circle?
Yes Ma’am
Very good students!
You already familiar with the parts
of a circle. Now we have to
familiarize also the equation of a
circle which is our topic for today.
The standard form of the equation of a
circle with its center at the origin is:
x2  y2  r 2
r is the radius of the circle so if we take
the square root of the right hand side,
Student’s are listening in the
we'll know how big the radius is.
discussion.
Notice that both the x and y terms are
squared. When we looked at
parabolas, only the x term was
squared.
Let's look at the equation
2
2
x  y 9
9 is r2 so r = 3
The center of the circle is at the origin
and the radius is 3. Let's graph this
circle. Show it in the presentation.
If the center of the circle is NOT at the
origin then the equation for the
standard form of a circle looks like this:
x  h 2   y  k 2  r 2
The center of the circle is at (h, k).
x  32   y  12  16
The center of the circle is at (h, k)
which is (3,1).
The radius is 4.
If you take the equation of a circle in
standard form for example:
x  22   y  42  4
Remember center is at (h, k) with (x h) and (y - k) since the x is plus
something and not minus, (x + 2) can
be written as (x - (-2)).
You can find the center and radius
easily. The center is at (-2, 4) and the
radius is 2.
x 2  y 2  4 x  8 y  16  0
D. Comparison and Contrast
What if the general form and
standard form will be given and
you will ask to find the center and
the radius, what would be the
process?
Do you still remember what is the
method of completing the square?
Solution:
By completing the square method,
we can get:
x2 - 4x + __ + y2 - 8y + __ = -16
What is the answer?
Will you answer it Jennifer?
Very Good!
So if we will going to simplify, the
standard form of a circle is
(x+2)2 + (y-4)2 = 42
The radius of the circle is 4 and C
(2,-4) is the center.
Now let's work some examples:
Yes ma’am
x2 + 4x + 4 + y2 - 8y + 16 = 16 + 4 + 16
Find an equation of the circle with
center at (0, 0) and radius 7.
Brenda what is the answer? Will
you write the answer on the board.
x  h 2   y  k 2  r 2
(x-0)2 + (y-0)2 = 72
Very Good!Let’s give her a yes
clap!
x2 + y2 = 49
1,2,3,..1,2,3 YES!
E. Generalization
What is the processs of finding the
equations of the circle and also the
center and radius?I will give
another example to further deepen
your understanding.
Find an equation of the circle with
center at (-2, 5) and radius 6.
Noemi will you answer this?
Excellent…
In our real life, I have a quote:
When you love, put a CIRCLE on it
instead of a heart, because a heart
is meant to be broken but a
CIRCLE lasts forever.
Yes Ma’am.
[(x-(-2)]2 + (y-5)2 = 62
(x + 2)2 + (y - 5)2 =36
IV. Evaluation
Find an equation of the circle written in general form
1. C (1,4); passes through (1, -1)
2. C (-1,-1); passes through (3, -1)
3. A diameter has endpoints (3,4) and (1,2)
V. Assignment
Find the center and radius of each circle.
4. 16x2 + 16y2 - 8x + 32y = 0
5. 4x2 + 4y2 - 24x – 16y + 36 = 0
6. 144x2 + 144y2 + 192x – 216y + 81 = 0
Prepared by:
LIGEA L. ARAMBULO, EdD
Head Teacher III (Math Department)
Checked by:
BELINDA S. MONDERO, EdD
Principal III, School Head Consultant in Mathematics
Noted:
LONGINO D. FERRER, EdD
Public Schools District Supervisor