Public learning track
Advanced Cartesian Lines, Circles, and Tangent-Normal Systems
12th Grade · Math · Open Global Math
10 lessons
Goal
Analyze straight lines, general and standard forms of circles, and solve geometric problems involving tangents, normals, and intersections.
Featured Diagrams
Point-Slope and General Linear Equations in Cartesian Space
10 lessons
0 of 10 done
- 1Point-Slope and General Linear Equations in Cartesian SpaceUp nextStart
- 2Parallel and Perpendicular Line Criteria and Families of LinesPremiumNot started yet
- 3Perpendicular Distance from a Point to a LineNot started yet
- 4Standard Form of a Circle Centered at (h, k)Not started yet
- 5Converting General Circle Equations by Completing the SquareNot started yet
- 6Equations of Tangent Lines to Circles at a Given PointNot started yet
- 7Equations of Normal Lines to CirclesNot started yet
- 8Finding Tangents to a Circle from an External PointNot started yet
- 9Intersections of Lines and Circles: Secants and ChordsNot started yet
- 10Solving Real-World Geometric Boundary Problems with CirclesNot 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.