Equations of Circles and Parabolas
Students derive the equation of a circle using the Pythagorean Theorem and complete the square to find the center and radius. They also explore the geometric description of a parabola.
About This Topic
Students derive the equation of a circle using the Pythagorean Theorem and complete the square to find the center and radius. They also explore the geometric description of a parabola.
Key Questions
- How does the Pythagorean Theorem lead to the standard equation of a circle?
- How can completing the square help us graph a circle from its general equation?
- What is the geometric definition of a parabola using a focus and directrix?
Active Learning Ideas
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Planning templates for Geometry
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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