Cricle.pptx
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The document outlines the definition and properties of circles in mathematics, including the general equation of a circle and methods to find its equation based on known parameters. It also provides formulas for the equation of circles formed by a diameter given two points, as well as discussing tangents and normals to circles. Additionally, it touches on solving linear equations related to circles.
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- 1. Dr. Ramkrishna Singh Solanki Asst. Professor: Mathematics and Statistics College of Agriculture Balaghat 1 Unit: Circle
- 2. Definition A circle is defined as the locus of a point which moves is a plane such that its distance from a fixed point in that plane is always constant. The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. ( ) ( ) , |
- 3. Basics
- 4. Day to day life example
- 5. Topic: Equation of a circle whose center and radius are known
- 6. Topic: Equation of a circle whose center and radius are known Problem 1: Find out the equation of a circle when center and radius are known. Problem 2: Find out the center and radius when equation of a circle is known.
- 8. Q. (2)
- 9. Topic: General equation of a circle
- 10. x2 + y2 +2gx +2fy + c = 0 (1) x2 + y2 +2gx +2fy + c + g2 + f 2 c = g2 + f 2 c (2) (x2 +2gx + g2) + (y2 +2fy + f 2) = g2 + f 2 c (3) (x + g)2 + (y + f)2 = g2 + f2 c (4) {x (- g)}2 + {y (- f)}2 = (5) (x - h)2 + (y - k)2 = r 2 (compare with standard equation of circle) we get 2 2 2 c f g Topic: General equation of a circle The general form of the equation of a circle is x2 + y2 + 2gx + 2fy + c = 0 Centre = (-g, -f) and radius = , where g, f and c are constants. (x2 +2gx + g2) = (x + g)2 (a2 +2ab + b2) = (a + b)2 c f g 2 2 c f g redius r f g center k h 2 2 ) , ( ) , (
- 12. Given equation Compare with general equation We get g We get f We get c
- 14. Topic: Equation of circle whose diameters is line joining two points (x1, y1) & (x2,y2) The equation of the circle drawn on the straight line joining two given points (x1, y1) and (x2, y2) as diameter is (x x1)(x x2) + (y y1)(y y2) = 0 Q. Find the equation of the circle, the coordinates of the end points of whose diameter are (-1, 2) and (4, -3). Sol. Here, x1 = -1, y1 = 2 and x2 = 4, y2 = -3, so the equation of the required circle is (x x1)(x x2) + (y y1)(y y2) = 0 (x +1)(x 4) + (y 2)(y + 3) = 0 x2 - 4x +x -4 + y2 + 3y 2y 6 = 0 x2 + y2 - 3x + y 10 = 0
- 15. How to solve three linear equations with three unknowns? (1) (2) (3) (4) (5) (6) ( ) ( ) (7) (8) (4) (5)
- 16. Topic: Equation of a circle passing through three given points 25 8 17 (x, y)= (x, y)= (x, y)= General equation of a circle
- 17. Topic: Tangent and Normal to a given circle at given point 爐伍爐爐萎爐-爐萎爐爐 爐爛爐萎じ爐鉦ぎ爐鉦え爛爐 爐伍爐爐萎爐謹爛爐爐
- 18. 1. Angle of bisectors between two lines 2. Condition of tangency of a line y = mx + c to the given circle x2 + y2 = a2