1. Recognise and use x2 + y2 = r2
Grade 9
Equation of a circle
Recognise and use x2 + y2 = r2
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Recognise and use the equation for a circle x2 + y2 = r2
Grade 9
Prior Knowledge
Surds
Circle vocabulary
Pythagoras’ Theorem
Duration
40 minutes are need to cover the objective.
Resources
Print slides: 4, 5, 15
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Link plotting equation of a circle with the form of the equation.
Give students slide 4 printed. Ask to substitute into the equation to complete the table of values. Discuss with students why there are two solutions for y. Once plotted – discuss the shape and the find the radius. Link to the objective. 15
Understand how to find the radius of circles with centre (0, 0)
Give students slide 5 printed. Discuss the general form for the question of a circle. Use this to write equations and sketch circles. Use slides 6 to 14 to discuss each question.
Recognise and use the equation for a circle x2 + y2 = r2 in contextualised problems
Give students slide 15 printed. Students to work independently on the two questions before reviewing collectively.
Students need to complete further learning related to the tangent and perpendicular before attempting exam questions. All specimen paper questions cover all aspects of circle geometry at this level. 10
Next Steps
Tangents and perpendicular lines
Assessment
PLC/Reformed Specification/Target 9/Algebra/Equation of a circle

3. Key Vocabulary
Equation Circle Origin Radius Diameter Centre

4. Plot this graph x2 + y2 = 25 x -5 -4 -3 3 4 5 Student Sheet 13 4 5
y (positive)
y (negative)
Student Sheet 1

5. The equation of a circle
centre (0, 0)
radius r
x2 + y2 = r2 .
centre (0, 0)
radius 5
Equation:
Write down the centre and radius of the circle with equation
x2 + y2 = 40
x2 + y2 = 45
Draw the circle with equation
x2 + y2 = 81
x2 + y2 = 100
Write down the equation of this graph
Student Sheet 2

6. The equation of a circle
The equation of this circle with centre (0, 0) and radius r is x2 + y2 = r2 .
radius
Centre (0,0)
x axis
y axis

7. The equation of a circle
The equation of this circle with centre (0, 0) with radius 5 is x2 + y2 = 52 or x2 + y2 = 25.
radius
Centre (0,0)
x axis
y axis 5 -5 5 -5

8. The equation of a circle
Write down the centre and radius of the circle with equation x2 + y2 = 40
radius
Centre (0,0)
x axis
y axis
Centre (0,0)
Radius √40 = 2 √10

9. The equation of a circle
Write down the centre and radius of the circle with equation x2 + y2 = 45
radius
Centre (0,0)
x axis
y axis

10. The equation of a circle – now you try
Write down the centre and radius of the circle with equation x2 + y2 = 45 .
radius
Centre (0,0)
x axis
y axis
Centre (0,0)
Radius √45 = 3 √5

11. The equation of a circle
Draw the circle with equation x2 + y2 = 81
radius
Centre (0,0)
x axis
y axis 9 -9

12. The equation of a circle – now you try
Draw the circle with equation x2 + y2 = 100
radius
Centre (0,0)
x axis
y axis 10
-10

13. The equation of a circle
Write down the equation of this graph
radius
Centre (0,0)
x axis
y axis 12
-12

14. The equation of a circle
Write down the equation of this graph
x2 + y2 = 144
radius
Centre (0,0)
x axis
y axis 12
-12

15. Problem Solving and Reasoning
AB is the diameter of a circle.
A is (6, 8) and B is (-6, -8).
Work out the equation of the circle.
What is the length of the diameter of a circle with the equation x2 + y2 = r2 ?
Student Sheet 3

16. Problem Solving and Reasoning
AB is the diameter of a circle.
A is (6, 8) and B is (-6, -8).
Work out the equation of the circle.

17. Problem Solving and Reasoning
AB is the diameter of a circle.
A is (6, 8) and B is (-6, -8).
Work out the equation of the circle.
Use Pythagoras’ theorem = 102
radius = 10
Equation is x2 + y2 = 144

18. Problem Solving and Reasoning
What is the length of the diameter of a circle with the equation x2 + y2 = r2 ?

19. Problem Solving and Reasoning
What is the length of the diameter of a circle with the equation x2 + y2 = r2 ?
Radius = r therefore, the diameter = 2r