Equation of a Circle

Presented by:Herminia R. Miralles

Ismael Mathay Sr. High School

Introduction:

Level: Third Year Duration: 55mins Mode: Group Work

Objectives:

At the end of the lesson the students should be able to:

Name the Parts of a Circle Determine relationships between Lines and

Circles. Write the Equation of a circle on a coordinate

plane.

Observation:

1. Look around the classroom in your notebook write down all the things that are round and looks like a circle.

2. Compare the things you have observed by the observation that your classmate made.

Are there similar things you have listed compare to your classmate?

3. Discuss among yourself what is a circle?

Circles

A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle.

Circle name by its center. What is the name of the

circle in the figure?

.P

Parts of a Circle

A radius is a segment from the center of the circle to a point on the circle. (CP)

A chord is a segment whose endpoints lie on the circle. (AB)

.P

A

B

C

Equation of Circles

Look at the graph of a circle in example #1 and example #2.

Example 1: Circle with center (0,0), radius 4

What is the difference between the two circles?

Example 2 : Circle with center (2,-5), radius 3

Graph:Graph

To write an Equation of a Circle Using Center- radius form: If center is at the origin. X2 + Y2 = r2 where r is the radius. 1. What is the center and and radius of the circle? Center (0,0), r = 4. 2. What is the equation of given

graph of the circle given in the figure? X2 + Y2 = 42

or X2 + Y2 = 16

3. What is the center and radius given in the figure?

4. What is the equation of a circle in the figure?

Answers:

C ( 0,0), r = 5

X2 + Y2 = 52 or X2 + Y2 = 25

5. Write the equation for the circle shown below if it is shifted 3 units to the right and 4 units up. What is the new center and radius?

What did you noticed about the Center? Circle whose radius not at the center.

A shift of 3 units to the right and 4 units up places the center at the point (3, 4). The radius of the circle can be seen from the graph to be 5.

Equation:

( x-3)2 + ( y -4)2 = 25

Standard Equation of a circle

In general, an equation for a circle with center at (h,k) and radius of r units is

(x-h)2 + (y-k)2 = r2

more examples

Examples:

1. What is the equation of the circle pictured on the graph below?

Answer

Answer:

1. Since the radius of this this circle is at its center is (0,0) , this circle's equation is (X-O)² +(Y-O)² = 1²

X² + Y² = 1

2. Look at the graph below, can you express the equation of the circle in standard form?

Answer

Answer;

2. Since the radius of this this circle is 1, and its center is (1,0), this circle's equation is

(X-1)² +(Y-0)² = 1 ²

(X-1)² + Y² = 1

3. Write the equation of a circle whose diameter has endpoints (4, -1) and

(-6, 7). 1. How do u get the center ?Find the center by using the midpoint formula.

2. How do you find the radius?

Find the radius by using the distance formula.

Points (-6,7) and (-1,3) were used here. (d = distance, or radius)

Equation: (x+1)2 +(y-3)2 =√41

ExercisesA. What is the radius of the circles

1. X2+Y2 =9 2. X2+Y2 =16 3. X2+Y2 =25 4. X2+Y2 =36 5. X2+Y2 =49

B. Radius of Circles1. 3 2. 4 3. 5 4. 6 5. 7

D. Write an equation of the figure given below.

C. Write an Equation of a circle given the following:

Center and Radius.1. C(0,0), r = 122. C ( 0,0), r = 103. C ( 2, 3), r = 54. C ( -4, 6), r=95. C ( -2, -3), r = 8

Microsoft Office Word Document

Worksheet 2

1. Write about what you have learnt today and what do you gain from the topic discussed about Equation of a circle?

2. Prepare one last question you may want your classmates to answer regarding the lesson discussed.

3. Read and study about how to get an Equation of a circle using Standard Equation Form.

Assignment:

Read and study about how to get an Equation of a circle using standard form.