Conic Sections
Analysis of parabolas, ellipses, and hyperbolas using Cartesian and parametric equations. Students will explore the geometric properties and eccentricity of conics.
About This Topic
Analysis of parabolas, ellipses, and hyperbolas using Cartesian and parametric equations. Students will explore the geometric properties and eccentricity of conics.
Key Questions
- How does the eccentricity define the shape of a conic section?
- What are the geometric definitions of ellipses and hyperbolas?
- How do we find the equations of tangents and normals to conics?
Planning templates for Further Mathematics
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.
More in Geometry and Linear Spaces
Polar Coordinates and Curves
Graphing curves defined by polar equations and finding the area of regions bounded by polar curves. Students will convert between Cartesian and polar coordinate systems.
2 methodologies
Matrix Algebra and Linear Spaces
Operations with matrices, determinants, and the inverse of a 3x3 matrix. Students will apply matrix algebra to solve systems of linear equations and understand linear dependence.
2 methodologies
Eigenvalues and Eigenvectors
Calculation and interpretation of eigenvalues and eigenvectors for square matrices. Students will explore diagonalisation and its applications to powers of matrices.
2 methodologies