STANDARD FORM OF A CIRCLE (center at (h, k) and (center at 0,0) with radius r

1. 36 - 12
Perform the indicated
operation.

2. 𝟒 𝟐
operation.

3. 𝟐𝟓
operation.

4. 25 + 16
operation.

5. 13 x 4
operation.

Imagined that you live
on this two
dimensional surface.
As you move outward
from the center,
everything gets
smaller--including
yourself. Would you
ever reach the edge of
your “universe”?

On a grid map of Cavite province, the coordinates that
corresponds to the location of a cellular phone tower is at
the (-6, 3) and it can transmit signal up to 12 km radius.
Also the coordinates of some towns in Cavite are shown.
1. How far is
the town of
Naic from the
Tower? Town
of General
Aguinaldo?
Town of
Maragondon?

1. How far is
the town of
Naic from the
Tower? Town
of General
Aguinaldo?
Town of
Maragondon?
1. Naic is 13 km away from the tower. General
Aguinaldo is 4 km away and Maragondon is
𝟐𝟎 or 𝟐 𝟓 km form the tower.

2. How were
you able to
determine
the distance
of one town
to the tower?

2. How were
you able to
determine
the distance
of one town
to the tower?
2. By using the distance formula
(𝑥2 − 𝑥1)2+(𝑦2−𝑦1)2.

3. In which town
can the tower
transmit signal?
In which town
the tower
cannot transmit
signal? Why?

3. In which town
can the tower
transmit signal?
In which town
the tower
cannot transmit
signal? Why?
3. The tower can transmit signal to the towns
of General Aguinaldo and Maragondon. The
signal cannot be transmitted to Naic because
it is 13 km away from it.

4. From the
activities you have
done, can you give
the equation that
represents the
transmission
boundaries of the
tower to any town?
Are you ready to
learn about the
equation of a
circle?

a. Illustrate standard form of the equation
of a circle;
b. Write the center-radius form of the
equation of a circle;
c. Solves problems involving geometric
figures on the coordinate plane.
d. Appreciate the use of equation of a circle
in finding solutions to real-life problems
and decision making.
OBJECTIVES

The Standard Form of the Equation of
a Circle
The standard equation of a circle with
center at (h, k) and a radius of r units is
The values of h and k indicate that the circle
is translated h units horizontally and k units
vertically from the origin.
I f the center of the circle is at the origin, the
equation of the circle is

STANDARD FORM OF A CIRCLE (center at (h, k) and (center at 0,0) with radius r

Illustrative Example:
Write the equation of a circle in
standard form that represents the
transmission signal of the cellular
phone tower to the town of
(1) Naic;
(2) General Aguinaldo;
(3) Maragondon.

Example 1 (Naic):
The equation of a circle with center
(Tower) at (-6, 3) and a radius
(distance of the town from the tower)
of 13 km is
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 𝟏𝟑 𝟐
or
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 169

Example 2 (General Aguinaldo):
at (–6, 3) and a radius of 4 km is
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 𝟒 𝟐
or
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 16

Example 3 (Maragondon):
at (–6, 3) and a radius of 𝟐𝟎 or 𝟐 𝟓
km is
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 𝟐 𝟓
𝟐
or
(𝒙 + 𝟔) 𝟐
+ (𝒚 − 𝟑) 𝟐
= 20

Example 4:
(Example of equation of a circle in
standard form with the center at the
origin)
at the origin and a radius of 4 units
is
𝒙 𝟐
+ 𝒚 𝟐
= 𝟒 𝟐
or
𝒙 𝟐
+ 𝒚 𝟐
= 16

Example 5:
(Example of equation of a circle in
standard form with the center at the
origin)
𝒙 𝟐
+ 𝒚 𝟐
= 𝟓
𝟐
or
𝒙 𝟐
+ 𝒚 𝟐
= 5
at the origin and a radius of 15 units
is

a. What is the center-radius form of
the equation of a circle in standard
form?
b. How do you write the equation of a
circle, given its radius, if the center is
at the origin?
c. How about if the center is not at
(0,0)?

Answer the following by completing the
missing part of the solution.
2 8 7 -2 8
-2 8 7
2 8 49

3-11 𝟏𝟏 3 -11
𝟏𝟏3 -11
11-3 +11

0 0 𝟐 𝟑 0 0
𝟐 𝟑
𝟏𝟐

Lot’s a Pizza shop offers three different sizes of
pizza. Suppose that the coordinates of the center
and the measure of the radius of each pizza are
as follows, write the equation of the circle of
each pizza in standard form.

Answer the following. What is the
equation of the circle in standard form?
a. The center of a circle is at the origin and
its radius is 12 units. What is the equation
of the circle?
b. The radius of a circle is 𝟑 𝟐 units and its
center is at (-2, 4). Find the equation of the
circle.
c. The diameter of a circular garden in
Rosario National High School is 8 meters
and its center is at (11, -10). Write the
equation of the circular garden.

ANSWER ON YOUR DRAWING BOOK AT HOME

Answer the given problem:
a. Pancit Malabon is one of the specialty served
in Chibugan Restaurant at Rosario, Cavite.
Their Pancit is available in 3 different bilao
sizes. Small whose center is at the origin and
has a radius of 10cm, Medium whose center is
at (-2, 5) and radius of 25 cm, and large with 40
cm radius and center at (13,0). Find the
equation of the circle of the different bilao
sizes in standard form.
b. What is the equation of a circular table
whose center lies at (1,2) and which passes
through (-3,5)?

1. Which of the following equation
describes a circle on the coordinate plane
with a center (2, -3)at and a radius of 5
units?
DIRECTIONS: Read and understand the
questions and write the letter of the
correct answer.

2. What is the equation of the circle
whose center is at (h, k)?
correct answer.
a.
b.
(𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐−𝒚 𝟏) 𝟐
c.
d.
𝒙 𝟏 + 𝒙 𝟐
𝟐
,
𝒚 𝟏 + 𝒚 𝟐
𝟐

2. What is the equation of the circle
whose center is at (0, 0)?
correct answer.
a.
b.
(𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐−𝒚 𝟏) 𝟐
c.
d.
𝒙 𝟏 + 𝒙 𝟐
𝟐
,
𝒚 𝟏 + 𝒚 𝟐
𝟐

4. A radius of a circle has endpoints
(-4, 3) and (1, -2) . What is the
equation that defines the circle if its
center is at the second quadrant?
correct answer.

5. Suppose the signal of Bombo Radio, Tacloban
can transmit messages up to a distance of 15 km.
If the radio signal’s origin is located at a point
whose coordinates are (1, 5), what is the equation
of the circle that defines the boundary up to
which the messages can be transmitted?
a. x 2 + y 2 – 2x – 10y – 199 = 0
b. x 2 + y 2 – 2x + 10y – 199 = 0
c. x 2 + y 2 + 2x – 10y – 199 = 0
d. x 2 + y 2 – 2x – 10y + 199 = 0
correct answer.

STANDARD FORM OF A CIRCLE (center at (h, k) and (center at 0,0) with radius r

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