Lesson Plan

• Write the equation of a circle given its centre (a,b) and radius r.
• Identify the centre and radius from equations presented in standard, general, or expanded form.
• Convert between standard, general, and expanded forms by completing the square.
• Validate a circle equation by confirming the radius expression is positive.

• Whiteboard and markers
• Projector or interactive display
• Printed worksheet with practice questions
• Graph paper and rulers
• Scientific calculators
• Handout of example circle equations

Begin by reminding students how to complete the square to rewrite quadratic expressions. They already know how to expand squares and solve simple equations, which will help them read circle equations quickly. Explain that by the end of the lesson they will be able to write, read, and convert circle equations and check their validity.

1. Do‑now (5'): Quick worksheet on completing the square – teacher checks answers.
2. Mini‑lecture (10'): Introduce standard and general forms, show how the centre and radius are read directly.
3. Guided example (10'): Work through the sample problem $x^2+y^2-6x+8y-11=0$ step‑by‑step.
4. Pair activity (12'): Students convert given expanded equations to standard form and record centre & radius.
5. Class discussion (8'): Highlight common mistakes (sign errors, forgetting the square root, checking $g^2+f^2-c>0$).
6. Exit ticket (5'): Each student writes the equation of a circle with a given centre and radius and identifies centre/radius from a new equation.

Summarise the key steps for reading and converting circle equations and remind students of the checklist for avoiding typical errors. Collect the exit tickets as a formative check and assign the worksheet problems as homework for further practice.