1.1 In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ;-6) respectively. ya A(4 ; 4) B(2;- 6) 1.1.1 Detemine the coordinates of O, the centre of the circle. 1.1.2 Calculate the length of the radius of the circle. 1.1.3 Write down the equation of the circle in form; (x – a)² + (y – b)² = p²

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.7: Dilations
Problem 15E
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Analytical geometry
Learning Activity 1
1.1 In the diagram below, a circle with centre O is given with diameter AB. The
coordinates of A and B are (4 ; 4) and (2 ; –6) respectively.
A(4 ; 4)
B(2;-6)
1.1.1 Determine the coordinates of O, the centre of the circle.
1.1.2 Calculate the length of the radius of the circle.
1.1.3 Write down the equation of the circle in form; (x – a)² + (y – b)² = r²
1.1.4 Write down the equation of the circle in form; ax² + bx + cy² + dy + e = 0
1.2 Determine the equation of the circle:
1.2.1 With centre the origin and a radius of 7
122 With centre the origin and passing through the point (8 ; – 3)
1.23 With centre (3 ; – 5) and a radius of /3
1.2.4 With diameter CD, where the coordinates of C and D are (0; - 3) and (2 ; 9)
respectively
1.2.5 With x intercepts (2 ; 0) and (– 4 ; 0) and a radius of 5
1.2.6 Passing through the points (2 ; 3) and (2 ; – 1), with radius v3
1.2.7 Passing through the points (2 ; – 2), (0 ; 1) and (1 ; 0)
1.2.8 Passing through the point (– 6 ; 1) with a circumference 12n and centre on
the y-axis.
Transcribed Image Text:Analytical geometry Learning Activity 1 1.1 In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ; –6) respectively. A(4 ; 4) B(2;-6) 1.1.1 Determine the coordinates of O, the centre of the circle. 1.1.2 Calculate the length of the radius of the circle. 1.1.3 Write down the equation of the circle in form; (x – a)² + (y – b)² = r² 1.1.4 Write down the equation of the circle in form; ax² + bx + cy² + dy + e = 0 1.2 Determine the equation of the circle: 1.2.1 With centre the origin and a radius of 7 122 With centre the origin and passing through the point (8 ; – 3) 1.23 With centre (3 ; – 5) and a radius of /3 1.2.4 With diameter CD, where the coordinates of C and D are (0; - 3) and (2 ; 9) respectively 1.2.5 With x intercepts (2 ; 0) and (– 4 ; 0) and a radius of 5 1.2.6 Passing through the points (2 ; 3) and (2 ; – 1), with radius v3 1.2.7 Passing through the points (2 ; – 2), (0 ; 1) and (1 ; 0) 1.2.8 Passing through the point (– 6 ; 1) with a circumference 12n and centre on the y-axis.
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