Chuong III 4 Duong tron

<span class='text_page_counter'>(1)</span>Teacher: Bui Thi Duyen Le Quy Don high school.

<span class='text_page_counter'>(2)</span> Check up 1. Write the formula of calculated distance between two points I(a;b) and M(x;y)? IM .  x  a. 2.   y  b. 2.

<span class='text_page_counter'>(3)</span> 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)?. y A 3 B. I O 2. 5 D. (C) IA 2 10  R  A  (C ). IB 5 R  B  (C ).. ID  2  R  D  (C ).. x.

<span class='text_page_counter'>(4)</span> §2. CIRCLE EQUATIONS 1. Circle equations with given center and radius.. y. State condition for M(x; y)  the (C)point IMM(x;y) = R is on the circle (C)? 2. 2. 2.   x  a    y  b  R  1. M(x;y). (1) is called the equation of the circle with center I(a;b) and radius R.. I R O. x. Example the equation ofcircle the circle center Example11: :Write The equation of the withwith center I(2; -I(2; 3) - 3) 2 2 and andradius radiusRR==55. is:  x  2    y  3 25 Note: The equation of the circle with the origin O as its 2 2 2 . center and radius R is x  y R.

<span class='text_page_counter'>(5)</span> 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(-3;4) b) With diameter AB.. y. x. O A(3;-4).

<span class='text_page_counter'>(6)</span> Example 3: Match each equation in A with a suitable circle in B. A. Equation 1 (x + 2)2 +(y - 6)2 = 1 2 (x - 1) + y = 25 2. 2. 3 x + y = 3/2 2. 2. 4 4x2 + (2y + 6)2 = 16. B. Circle. a Center (0; -3), radius R = 2 b Center (0; 0), radius. 6 R 2. c Center (-2; 6) , radius R = 1 d Center (0; -6), radius R = 4 e. Center(1; 0), radius R = 5.

<span class='text_page_counter'>(7)</span> the equation (1)? 2. Develop Comments 2 2 2.  x  a 2. 2.   y  b  R (1). 2. 2. 2.  x  y  2ax  2by  a  b  R 0 2 2  x  y  2ax  2by  c 0(2) , where c a 2  b 2  R 2 . 2. 2. (2)   x  a    y  b  a 2  b 2  c. When is (2) equation of the circle?. 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) 2 2 and radius R  a  b  c.

<span class='text_page_counter'>(8)</span> Example 4:Given the equation: x 2  y 2  4 x  6 y  3 0. Is this a circle equation?If it is, find the center and radius of the circle?.

<span class='text_page_counter'>(9)</span> 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..

<span class='text_page_counter'>(10)</span> 1. 2. 3. Lucky Star 4. 6 5.

<span class='text_page_counter'>(11)</span> Question 1. Given the equation: 2 x 2  y 2 – 8 x  2 y  1  0 (1) 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).. 10 15 14 13 12 11 9 8 7 6 5 4 3 2 1.

<span class='text_page_counter'>(12)</span> Question 3 Which of the following is the circle equation? (A) x 2  2y 2 – 4x – 8 y +1  0 (B) x 2  y 2 – 4x  6y + 20  0 (C) 4 x 2  y 2 – 10x  6y  2  0 2 2 (D) x  y – 4x  6y  12  0. 10 15 14 13 12 11 9 8 7 6 5 4 3 2 1.

<span class='text_page_counter'>(13)</span> Congratulations! You’ve just got a lucky star!. 10 points.

<span class='text_page_counter'>(14)</span> Question 4 2. 2. 10 15 14 13 12 11 9 8 7 6 5 4 3 2 1. Given the circle (C): x  y  2x + 4y – 20  0 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)..

<span class='text_page_counter'>(15)</span> Question 2. 10 15 14 13 12 11 9 8 7 6 5 4 3 2 1 The circle (C): x 2  y 2  x + y –1  0 with center I and radius R is:. ( A) I ( 1;1), R 1; 6 1 1 (B) I  ;   , R  ; 2  2 2 6  1 1 (C ) I   ;  , R  ; 2  2 2 ( D) I ( 1;1), R  6..

<span class='text_page_counter'>(16)</span> Congratulations! You’ve just got a lucky star!. 10 points.

<span class='text_page_counter'>(17)</span> Consolidation 1. The equation of the circle with center I(a;b) and radius R is.  x  a 2. 2. 2.   y  b  R 2 (1) 2. 2. The equation: x  y  2ax  2by  c 0(2) is the equation of the circle (C) if and only if a 2  b 2  c  0. 2 2 R  a  b c 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”..

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