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Unité 3Lesson 8
Circle equation
What are we going to learn in this lesson?
• Transformational form, standard form and general form of a circle and how to convert between these 3 forms.
• Completing the square.
• Mapping notation for a circle
• How to find the centre and the radius of a circle.
• How to graph circle on a Cartesian plan.
• Transformational form and general form of a ellipse and how to convert between these 2 forms.
• How to determine the centre and the symmetrical axes of an ellipse.
• Mapping notation for an ellipse.
• How to represent ellipses in a Cartesian plan.
Circle equation
They are 3 different methods to represent a circle.
1. Transformational form
2. Standard form
3. General form
centre C(p,q)radius r
Example1. Find the centre and the radius of the following circles:
a) b)
Example2. Find the centre and the raidus, then convert into the standard form and general form.
Example3. Give the equation (in standard form) of a circle with...
a) a radius of 4 and centre C(3,6).
b) a centre C(3,2) and that goes through the point (6, 2).
Example4. State the centre and radius, then graph the circle.
14 12 10 8 6 4 2 0 2 4 6 8
4
2
2
4
6
8
10
12
x
y
Example5. State the centre, the radius and the mapping notation, and then graph the circle.
1 0 1 2 3 4 5
2
1
1
2
3
4
x
y
Example6. State the centre, the radius and the mapping notation, and then graph the circle.
10 8 6 4 2 0 2 4 6 8 10
8
6
4
2
2
4
6
8
x
y
Example7. State the centre, the radius and the mapping notation, and then graph the circle.
7 6 5 4 3 2 1 0 1 2 3
2
1
1
2
3
4
5
6
7
8
x
y
Example8. State the centre, the radius and the mapping notation, and then graph the circle.
10 9 8 7 6 5 4 3 2 1 0 1 2
4321
123456789
x
y
WorksheetOmnimaths 12 p. 141
#s 3,7
#s 10,14,15 (transformational form as well )
#s 17,19,22,26 (General form as well)
#s 27, 29, 30 (mapping notation as well)
#s 32, 34 (General form as well)
#s 3639 (transformational form as well)
# 62
Ellipse equation
They are 3 different methods to represent an ellipse.
1. Transformational form
2. Standard form
3. General form
Important terms:• Major axis The longer axis.
• Minor axis The shorter axis.
centre C(p,q)
length of axis 2a and 2b
Example1. Find the centre and the length of the major and minor axes:
a) b)
Example2. Find the centre, the length of the major and minor axes, and then graph the ellipse.
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
87654321
12345678
x
y
Example3. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
6 4 2 0 2 4 6
6
4
2
2
4
6
x
y
Example4. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
9 8 7 6 5 4 3 2 1 0 1 2
5
4
3
2
1
1
2
3
4
5
x
y
Example5. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
87654321
12345678
x
y
Exercice
Omnimaths 12p. 150 # 14
# 6, 7, 9, 25, 26
only a and b
For the 2nd set of questionsDo part a and b then ...• graph the ellipse• give the transformational form• give the mapping notation