WELCOME ALL TEACHERS TO CLASS 10D1
LESSON 2: CIRCLE EQUATIONS
Teacher: Bui Thi Duyen
Le Quy Don high school
Check up
1. Write the formula of calculated distance between two points I(a;b) and M(x;y)?
I
2
3
(C)
5
B
D
2. Oxy, given the circle (C) with center I(2;3) and radius R=5. A(-4;5), B(-2;0), D(3;2)? Find point on the circle (C)?
M(x; y) (C) IM = R
1. Circle equations with given center and radius.
(1) is called the equation of the circle with center I(a;b) and radius R.
Example 1: The equation of the circle with center I(2; - 3) and radius R = 5 is:
Note: The equation of the circle with the origin O as its center and radius R is
.

§2. CIRCLE EQUATIONS
State condition for the point M(x;y) is on the circle (C)?
Example 1: Write the equation of the circle with center I(2; - 3) and radius R = 5 .
B(-3;4)
y
x
O
A(3;-4)
Example 2: Given two points A(3;-4), B(-3;4).
Write the equation of the circle (C):
a) With center A and pass through B.
b) With diameter AB.
Example 3:
Match each equation in A with a suitable circle in B.
Conclusion: (2) is the equation of the circle (C) if and only if a2 + b2 – c > 0. Then the circle has center I(a; b) and radius
Develop the equation (1)?
2. Comments
When is (2) equation of the circle?
Example 4:Given the equation:

Is this a circle equation?If it is, find the center and radius of the circle?
Game: “Lucky Star”

The rules: There are 6 stars on the screen. Each group will take turns to choose a star you like and answer the questions inside it.
If your answer is correct, you will get 10 points, if not the chance will be given to other groups.
However, if you choose a lucky star, you will get 10 points without having to answer any question.

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Lucky Star
2
Given the equation:
Choose the correct answer among A, B, C or D.

A. (1) isn’t equation of circle.
B. The circle (1) has center I(4; -1).
C. The circle (1) has radius R = 3.
D. The circle (1) has center I(-4; 1).


Question 1
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Question 3
Which of the following is the circle equation?
(A)

(B)

(C)

(D)
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Congratulations! You’ve just got a lucky star!
10 points

Given the circle (C):
Find the wrong proposition in the following propositions:
(A) The circle (C) has center I(1; 2);
(B) The circle (C) has radius R = 5;
(C) The circle (C) passes through the point M(2; 2);
(D) The circle (C) does not pass through the point A(1; 1).
Question 4
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The circle (C):
with center I and radius R is:


Question 2
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Congratulations! You’ve just got a lucky star!
10 points
Consolidation
The equation of the circle with center I(a;b) and radius R is
2. The equation:
is the equation of the circle (C) if and only if
Then the circle has center I(a; b) and radius
Homework:
Do exercises 1 – 5 / page 83, 84
Prepare for the next part of this lesson: “ The equation of a tangent to a circle”.
Thank you for your attention!