Recognise and use x2 + y2 = r2 Grade 9 Equation of a circle Recognise and use x2 + y2 = r2 If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk

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

Key Vocabulary Equation Circle Origin Radius Diameter Centre

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

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

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

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

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

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

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

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

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

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

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

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

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.

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 62 + 82 = 102 radius = 10 Equation is x2 + y2 = 144

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

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