Bài giảng Hình học 10 (Bài giảng bằng tiếng Anh) - Unit 2: Circle equations (lesson 1)

Collect by www.thuonghieuso.netCompany LogoWELCOME TO OUR CLASS – 10D Teacher: Dương Đức ThìnNinh Binh Department of Education and TrainingNHO QUAN C HIGH SCHOOLCollect by www.thuonghieuso.netCompany Logo Teacher: Dương Đức ThìnSome pictures of the circleClockCar wheelCoinsUNIT 2. CIRCLE EQUATIONS (LESSON 1) Circle equation with given center and radius1Comment2PracticeThe question of a fantgent to a circle (lesson 2)3Collect by www.thuonghieuso.netCompany Logo Teacher: Dương Đức Thìn Teacher: Dương Đức Thìn 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1)To specify the circle, which elements we need know?It is center and radius. Teacher: Dương Đức ThìnIn the Oxy plane, given the circle (C) with :+ Center (a;b)+ Radius R+ M(x,y) (C) M = Rif 1. Circle equation with given center and radiusRxobayMUNIT 2. CIRCLE EQUATIONS (LESSON 1)which condition is M satified? Teacher: Dương Đức Thìn (x – a)2 + (y - b)2 = R2 In the Oxy plane, given the circle (C) with :+ Center (a;b)+ Radius R+ M(x,y) (C) M = RThe equation (x – a)2 + (y - b)2 = R2 (1) is called the equation of the circle with center (a,b), radius R 1. Circle equation with given center and radiusRxobayMUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức ThìnExample 1. In the Oxy plane, the equation of the circle with the center I(2;-3), radius R = 4 is: A. B. C. D. 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức ThìnExample 2 . In the Oxy plane, given the circle (C): with center, radius is:A. Center I(3; -4), Radius R= 25B. Center I(-3; 4), Radius R= 25C. Center I(3; -4), Radius R= 5D. Center I(-3; 4), Radius R= 5 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức ThìnExample 3. Write the equation of the circle with the center I(1;4) and passes through B(2;6) >>> Group 1, 2Example 4. Write the equation of the circle has diameter AB with A(3;-2) and B(1;4). >>>Group 3, 4 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức ThìnExample 3. Write the equation of the circle with the center I(1;4) and passes through B(2;6)+ The radius of the circle is: + The equation of the circle is: BSolve 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức Thìn + The center of the circle is midpoint of AB+ The radius of the circle is: + The equation of the circle is: BA Example 4. Write the equation of the circle has diameter AB with A(3;-2) and B(1;4).Solve 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức Thìn+ The equation of the circle with center I(0; 0), radius R = is : Example 5. Note:The circle equation with center O(0;0) and radius R is: x2 + y2 = R2 1. Circle equation with given center and radiusUNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức Thìn+ The circle equation UNIT 2. CIRCLE EQUATIONS (LESSON 1)Comments2Develop (1) converter into the quadratic equation with x2 and y2 Teacher: Dương Đức Thìn+ The circle equation Can be rewritten in the form where UNIT 2. CIRCLE EQUATIONS (LESSON 1)Comments2Conditions exists of the equation x2 + y2 – 2ax – 2by + c = 0 Teacher: Dương Đức ThìnUNIT 2. CIRCLE EQUATIONS (LESSON 1)Comments2 1. The coefficients of x2 and y2 are same.2. a2 + b2 – c > 0. The equationx2 + y2 – 2ax – 2by + c = 0 (C) is the circle equation if and only if a2 + b2 – c > 0. Then, (C) has center I(a; b) and radius- The coefficients of x2 and y2 are same. Teacher: Dương Đức ThìnUNIT 2. CIRCLE EQUATIONS (LESSON 1)Comments2 Teacher: Dương Đức Thìn Example 1. In the following equations, the circle equation is:A. B. C.D. UNIT 2. CIRCLE EQUATIONS (LESSON 1)Comments2 Teacher: Dương Đức Thìn Example 2 . In the Oxy plane, given the circle (C): with center and radius is:A. Center I(-1; 2), Radius R=9 B. Center I(1; -2), Radius R=3 C. Center I(2; -4), Radius R=9 D. Center I(-2; 4), Radius R= 3Comments2UNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức Thìn Example 3. State which of the following is the circle equation?Find the centers and radius (if yes).a) 2x2 + y2 – 8x + 2y – 1 = 0.	 Group 1,2	b) x2 + y2 + 2x – 4y – 4 = 0. Group 1,2c) x2 + y2 – 2x – 6y + 20 = 0	 Group 3,4	d) x2 + y2 + 6x + 2y + 9 = 0. Group 3,4Comments2UNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức Thìn Example 3. State which of the following is the circle equation?Find the centers and radius (if yes).a) 2x2 + y2 – 8x + 2y – 1 = 0.	 	b) x2 + y2 + 2x – 4y – 4 = 0. c) x2 + y2 – 2x – 6y + 20 = 0	 	d) x2 + y2 + 6x + 2y + 9 = 0 No, because the coefficients of x2 and y2 are differentNo, because a2 + b2 – c < 0. Center I(-1;2), radius R = 3Center K(-3;-1), radius R = 1Comments2UNIT 2. CIRCLE EQUATIONS (LESSON 1) Teacher: Dương Đức ThìnSUMMARY1. Circle equation with given center and radius2. Identification the circle equation If , then the equation (2) is the circle equationwith center , radius with center , radius R Trong khoa học kỹ thuật người ta vận dụng phương trình đường tròn để đưa ra quỹ đạo bay của một vệ tinh bay rất gần trái đất, cách tâm trái đất một khoảng không đổi.Toán học và thực tiễn Teacher: Dương Đức ThìnSuppose: Earth's artificial satellites fly very close to the earth in a circle orbit, about 1,000 km (Earth's radius about 6400 km). Know that at some point the center of the earth is at coordinates I(1; 2). Write equation orbit of satellites?Answer: (x-1)2 + (y-2)2 = 74002The real problem Teacher: Dương Đức ThìnSuppose: Earth's artificial satellites fly very close to the earth in a circle orbit, about 1,000 km (Earth's radius about 6400 km). Know that at some point the center of the earth is at coordinates I(1; 2). Write equation orbit of satellites?The circle equation: (x-1)2 + (y-2)2 = 74002The real problem Teacher: Dương Đức ThìnRadius R = 6400 + 1000 = 7400Giả sử: Vệ tinh nhân tạo của trái đất bay rất gần với trái đất theo quỹ đạo đường tròn, cách trái đất một khoảng 1000km (bán kính trái đất khoảng 6400Km). Biết rằng tại một thời điểm nào đó tâm của trái đất ở tọa độ I(1; 2). Viết phương trình quỹ đạo của vệ tinh?Đáp án: (x-1)2 + (y-2)2 = 74002Bài toán thực tế Teacher: Dương Đức Thìn