S5_Unit_2_Outcome_4 - www.mathsrevision.com Higher Outcome...

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Unformatted text preview: www.mathsrevision.com Higher Outcome 4 Higher Unit 2 www.mathsrevision.com www.mathsrevision.com The Graphical Form of the Circle Equation Inside , Outside or On the Circle Intersection Form of the Circle Equation Find intersection points between a Line & Circle Tangency (& Discriminant) to the Circle Equation of Tangent to the Circle Exam Type Questions Mind Map of Circle Chapter Finding distances involving circles and lines www.mathsrevision.com Higher Outcome 4 The Circle (a , b) (x , y) r (x , b) (x a) (y b) By Pythagoras The distance from (a,b) to (x,y) is given by r 2 = (x - a) 2 + (y - b) 2 Proof r 2 = (x - a) 2 + (y - b) 2 Feb 13, 2012 Feb 13, 2012 www.mathsrevision.com www.mathsrevision.com 3 3 Equation of a Circle Equation of a Circle Centre at the Origin Centre at the Origin 2 2 2 ) ( r y x = + By Pythagoras Theorem OP has length r r is the radius of the circle O x-axis r y-axis y x a b c a 2 +b 2 =c 2 P(x,y) www.mathsrevision.com Higher Outcome 4 x 2 + y 2 = 7 centre (0,0) & radius = 7 centre (0,0) & radius = 1 / 3 x 2 + y 2 = 1 / 9 Find the centre and radius of the circles below The Circle Feb 13, 2012 Feb 13, 2012 www.mathsrevision.com www.mathsrevision.com 5 5 General Equation of a Circle General Equation of a Circle x-axis y-axis a C (a , b) b O To find the equation of a circle you need to know r x y P(x, y) x-a y-b a b c a 2 +b 2 =c 2 By Pythagoras Theorem CP has length r r is the radius of the circle with centre (a,b) Centre C (a,b) and radius r 2 2 2 ) ( ) ( r b y a x =- +- Centre C(a,b) Centre C (a,b) and point on the circumference of the circle OR www.mathsrevision.com Higher Outcome 4 Examples (x-2) 2 + (y-5) 2 = 49 centre (2,5) radius = 7 (x+5) 2 + (y-1) 2 = 13 centre (-5,1) radius = 13 (x-3) 2 + y 2 = 20 centre (3,0) radius = 20 = 4 X 5 = 2 5 Centre (2,-3) & radius = 10 Equation is (x-2) 2 + (y+3) 2 = 100 Centre (0,6) & radius = 2 3 r 2 = 2 3 X 2 3 = 4 9 = 12 Equation is x 2 + (y-6) 2 = 12 NAB The Circle www.mathsrevision.com Higher Outcome 4 Example Find the equation of the circle that has PQ as diameter where P is(5,2) and Q is(-1,-6). C is ( (5+(-1)) / 2 , (2+(-6)) / 2 ) = (2,-2) CP 2 = (5-2) 2 + (2+2) 2 = 9 + 16 = 25 = r 2 = (a,b) Using (x-a) 2 + (y-b) 2 = r 2 Equation is (x-2) 2 + (y+2) 2 = 25 P Q C The Circle www.mathsrevision.com Higher Outcome 4 Example Two circles are concentric. (ie have same centre) The larger has equation (x+3) 2 + (y-5) 2 = 12 The radius of the smaller is half that of the larger. Find its equation....
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This note was uploaded on 02/13/2012 for the course MAT 205 math 205 taught by Professor Google during the Spring '10 term at University of Phoenix.

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S5_Unit_2_Outcome_4 - www.mathsrevision.com Higher Outcome...

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