Public learning track
Conic Sections: Loci, Standard Equations, and Optical Properties
12th Grade · Math · Open Global Math
9 lessons
Goal
Analyze parabolas, ellipses, and hyperbolas through planar conic cuts, focus-directrix-eccentricity locus definitions, and reflective applications.
Featured Diagrams
Conic Sections as Planar Cross-Sections of a Double Cone
9 lessons
0 of 9 done
- 1Conic Sections as Planar Cross-Sections of a Double ConeUp nextStart
- 2The Unified Focus-Directrix-Eccentricity Definition of ConicsPremiumNot started yet
- 3Parabolas: Focus, Directrix, Vertex, and Standard EquationsNot started yet
- 4Ellipses: Foci, Major-Minor Axes, and Standard EquationsNot started yet
- 5Hyperbolas: Foci, Axes, and AsymptotesNot started yet
- 6Converting General Second-Degree Conic Equations to Standard FormNot started yet
- 7Tangent Lines and Tangency Conditions for Conic SectionsNot started yet
- 8Reflective and Optical Properties of Conic SectionsNot started yet
- 9Modeling Orbital Mechanics and Engineering Structures with Conic SectionsNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
10 lessons
Advanced Cartesian Lines, Circles, and Tangent-Normal Systems
Analyze straight lines, general and standard forms of circles, and solve geometric problems involving tangents, normals, and intersections.
2
9 lessons
Conic Sections: Loci, Standard Equations, and Optical Properties
Analyze parabolas, ellipses, and hyperbolas through planar conic cuts, focus-directrix-eccentricity locus definitions, and reflective applications.
3
8 lessons
Parametric Equations: Plane Curves and Motion Modeling
Represent plane curves parametrically, eliminate parameters to obtain Cartesian equations, and model physical trajectory phenomena.
4
9 lessons
Polar, Cylindrical, and Spherical Coordinate Systems
Locate positions and convert equations between Cartesian, Polar $(r, \theta)$, Cylindrical $(r, \theta, z)$, and Spherical $(\rho, \theta, \phi)$ coordinates, and graph polar curves.