Unité 3
Lesson 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 ­
centre C(p,q)
radius r 2. Standard form ­
3. General form ­
Example
1. Find the centre and the radius of the following circles:
a)
b)
Example
2. Find the centre and the raidus, then convert into the standard form and general form. Example
3. 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).
Example
4. State the centre and radius, then graph the circle. y
12
10
8
6
4
2
x
­14 ­12 ­10
­8
­6
­4
­2
0
­2
2
4
­4
Example
5. State the centre, the radius and the mapping notation, and then graph the circle. y
4
3
2
1
x
­1
0
­1
­2
1
2
3
4
5
6
8
Example
6. State the centre, the radius and the mapping notation, and then graph the circle. y
8
6
4
2
x
­10
­8
­6
­4
­2
0
­2
2
4
6
8
10
­4
­6
­8
Example
7. State the centre, the radius and the mapping notation, and then graph the circle. y
8
7
6
5
4
3
2
1
x
­7
­6
­5
­4
­3
­2
­1
0
­1
­2
1
2
3
Example
8. State the centre, the radius and the mapping notation, and then graph the circle. y
9
8
7
6
5
4
3
2
1
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1
0
­1
­2
­3
­4
Worksheet
Omnimaths 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
x
1
2
Ellipse equation They are 3 different methods to represent an ellipse. 1. Transformational form ­
centre C(p,q)
length of axis 2a and 2b
2. Standard form ­
3. General form ­
Important terms:
• Major axis ­ The longer axis.
• Minor axis ­ The shorter axis.
Example
1. Find the centre and the length of the major and minor axes: a)
b)
Example
2. Find the centre, the length of the major and minor axes, and then graph the ellipse.
y
8
7
6
5
4
3
2
1
x
­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 ­10 1 2 3 4 5 6 7 8
­2
­3
­4
­5
­6
­7
­8
Example
3. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
y
6
4
2
x
­6
­4
­2
0
­2
­4
­6
2
4
6
Example
4. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
y
5
4
3
2
1
x
­9
­8
­7
­6
­5
­4
­3
­2
­1
0
­1
1
2
­2
­3
­4
­5
Example
5. Find the centre, the length of the major and minor axes, the mapping notation, and then graph the ellipse.
y
8
7
6
5
4
3
2
1
­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 ­10 1 2 3 4 5 6 7 8
­2
­3
­4
­5
­6
­7
­8
x
Exercice
only a and b Omnimaths 12
p. 150 # 1­4
# 6, 7, 9, 25, 26
For the 2nd set of questions
Do part a and b then ...
• graph the ellipse
• give the transformational form
• give the mapping notation