LESSON PLAN IN MATHEMATICS 10
I. OBJECTIVE
At the end of the lesson the students must be able to:
i. Illustrate the center-radius form of the equation of a circle.
M10GE-IIh-1
ii. Determine the center and radius of a circle given its equation and vice-versa. M10GE-IIh-2
iii. Solve real-life problems using equation of a circle.
II. SUBJECT MATTER
a) TOPIC: EQUATION OF THE CIRCLE
b) MATERIALS:
i. Sample problems/ illustrations
ii. Manila paper/ bond paper/Projector
iii. Chalk and marker
c) REFERENCES: curriculum guide, teachers guide grade 10, learners module grade 10
III. PROCEDURE
Teacher’s Activity
A. Preliminary activities
i. Checking of attendance
ii. Recall on solving perfect square trinomial and
square of a binomial.
 Good morning class!
 Ok! Our lesson for today is all about Equation
of the Circe but before we proceed to today’s
topic, there are some prerequisite concepts in
mathematics that you need to know first in
order for you to easily understand our new
topic.
 Are you ready class?
 Well then, let’s begin with this one!
ACTIVITY 1: make it perfect!
 Determine the number that must be added to
make each of the following a perfect square
trinomial. Then express each as a square of a
binomial.
2
1. 𝑥 + 4𝑥 + ________
2. 𝑡 2 + 10𝑡 + _______
3. 𝑟 2 − 14𝑟 + _______
1
4. 𝑠 2 + 3 𝑠 + _______
Student’s Activity
 Good morning ma’am!
 Yes ma’am!
1. 4; (𝑥 + 2)2
2. 25; (𝑡 + 5)2
3. 49; (𝑟 − 7)2
1
1 2
4. 36; (𝑥 + 6)
9
3 2
5. 64 ; (𝑥 − 8)
3
5. 𝑥 2 − 4 𝑥 + ______
 How did you determine the number that must
be added to each expression to produce a
perfect square trinomial?
 How did you express each resulting perfect
square trinomial into a square of a binomial?
B. Motivation
ACTIVITY 2: How far am I from my point of
rotation?
 Consider the given illustration and try to
answer the following.
 We divide the coefficient of the
second term to 2 then we square it.
 We factor the perfect square
trinomial into a form of (𝑎 ± 𝑏)2

Graph of the circle that passes through point
A(8,0) and centered at the origin.
 How far is point A from the center of the
circle?
 Very good!
 Does the circle pass through (0,8)?
(-8,0)?(0,-8)? Why?
 Excellent!
 What is the relation of the distance of point A
from the center of the circle?
 That’s correct!
 Suppose point M(-4,6) is another point on the
coordinate plane, is M a point on the circle?
Why? How about N(8,-5)?
 Correct!
 If a point is on the circle, how is its distance
related to the radius of the circle?
 Very good!
 What if you have to find the distance of a
given point from another point not on the
origin and are not vertically or horizontally
aligned on coordinate axes?
C. Presentation
Consider the given illustration and try to answer the
following questions.
 How far is point C from the center of the
circle?
 Very good!
 Does the circle pass through point (-2,7)?
(8,7)? (-3,-4)?
 Suppose another point M(-7,6) is on the
plane, is M a point on the circle? Why?
 8 units’ ma’am!
 Yes ma’am! Because they have the
same distance.
 It is the radius of the circle.
 No ma’am! Point M is inside of the
circle.
 Point N is outside the circle ma’am!
 The distance would be equal to the
radius ma’am!
 We will use the distance formula
ma’am!
𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
 √61 Or approximately 7.81 units
ma’am!
 Yes ma’am!
 No ma’am! Because it is outside the
circle.
 What is the distance of point M to the center
of the circle?
 Very good!
 What if we didn’t use a graph to determine
whether the given point is on the circle? What
other method we can use to tell whether a
point is outside, inside or on the circle?
 Very well said!
D. Lesson proper
Now that you know the prerequisite concepts in this
lesson, we can now proceed.
THE STANDARD FORM OF EQUATION OF THE CIRCLE
The standard form of equation of the circle is
given by (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2 where (h,k) is
the center and r is the radius of the circle.
If the center of the circle is at the origin, the
equation of the circle is given by 𝑥 2 + 𝑦 2 = 𝑟 2 .
Ex. 1 the equation of the circle with center at (2,7)
and a radius of 6 units.
Ex. 2 the equation of the circle whose center at the
origin and a radius of 4 units.
Ex. 3 the equation of a circle with center at
( -5, -9) and a radius of 10 units.
Ex. 4 the equation of a circle with center at
( 0, -9 ) and a radius of 3 units.
Ex. 5 the equation of a circle with center at
( 5 , 0) and a radius of 4 units.
Try these;
Illustrate the standard form of equation of the
circle given the following.
1. centered at (-2,4), radius is 5 units
2. centered at (1,2), passes through point (4,2)
Determine the center and the radius of the
following equation of the circle.
1. (𝑥 − 6)2 + (𝑦 − 9)2 = 121
2. (𝑥 + 4)2 + (𝑦 + 4)2 = 144
E. Generalization
Read the situation below and answer the following
problem.
Mount Mayon, an active volcano has a 10 km
danger zone located at (1,-2), Freya a simple
resident resides at a coordinate of A(-4,-9).
1. Is Freya still covered by the 10 km danger zone?
2. If she is still covered by the 10 km danger zone, at
what coordinate she need to go for evacuation, is
it (7,-10) or (-2,-12)? Calculate the distance of each
point from the center.
3. What is the equation of the circle?
 11.18 units ma’am!
 Compute for the radius of the given
circle and compare if the distance of
the asked point from the center of
the circle is equal to the distance of
the radius, if true, then the said
point is passed through by the circle
since any radius formed on a circle
has an equal distance.
 (𝑥 − 2)2 + (𝑦 − 7)2 = 62 or
(𝑥 − 2)2 + (𝑦 − 7)2 = 36
 𝑥 2 + 𝑦 2 = 42 or 𝑥 2 + 𝑦 2 = 16
( x + 5 )2 + ( y + 9 )2 = 100
x2 + ( y + 9 )2 = 9
( x -5 )2 + y2 = 16
1. (𝑥 + 2)2 + (𝑦 − 4)2 = 25
2. (𝑥 − 1)2 + (𝑦 − 2)2 = 25
1. center (6,9) , radius is 11 units
2. center is (-4,-4) , radius is 12 units
 (𝑥 − 1)2 + (𝑦 + 2)2 = 100
IV. EVALUATION
A. Illustrate the standard form of equation of the circle given:
1. The center is at (-1,3) and radius is 2.
answer:
(𝑥 + 1)2 + (𝑦 − 3)2 = 4
2. The center is at (-1,2) and radius is 8
answer:
(𝑥 + 1)2 + (𝑦 − 2)2 = 64
B. Determine the center and the radius of the following equation of the circle.
1. (𝑥 − 8)2 + (𝑦 − 7)2 = 225
answer: C=(8,7); r=15
2
2
2. (𝑥 + 2) + 𝑦 = 196
answer: C=(-2,0); r=14
V. ASSIGNMENT
Illustrate the standard form of equation of the circle given the following:
1. Centered at (-9,11) and passes through point L(-13,2)
2. Centered at (6,1) and passes through point (-9,4 )