Public learning track
Parametric Curves: Conversions and Geometric Trajectories
11th Grade · Math · Open Global Math
7 lessons
Goal
Model plane curves parametrically, convert between parametric and Cartesian representations, and analyze 2D kinematics, projectile motion, and cycloids.
Featured Diagrams
Parametric Equations of Plane Curves and Curve Orientation
7 lessons
0 of 7 done
- 1Parametric Equations of Plane Curves and Curve OrientationUp nextStart
- 2Converting Between Parametric and Cartesian FormsPremiumNot started yet
- 3Eliminating Trigonometric Parameters to Find Cartesian EquationsNot started yet
- 4Parametric Representations of Standard Conic SectionsNot started yet
- 5Modeling Projectile Motion with Parametric EquationsNot started yet
- 6Cycloids, Epicycloids, and Rolling Wheel CurvesNot started yet
- 7Optimization Problems Using Parametric EquationsNot started yet
Standards Covered
- OGM.12.GEO.4Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Understand and use parametric equations x = f(t), y = g(t) for plane curves, convert between Cartesian and parametric forms by eliminating the parameter, and use parametric models to represent motion and geometric trajectories.
- OGM.12.GEO.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Identify, represent, and analyze conic sections (parabolas, ellipses, hyperbolas) geometrically as cross-sections of a cone and algebraically in Cartesian, polar, and parametric forms; investigate geometric loci.
Curriculum Framework
11th Grade · Math · Open Global Math
1
8 lessons
Advanced Linear Coordinate Geometry and Distance Optimization
Master linear equations in general and point-slope forms, calculate perpendicular distances, analyze families of lines, and solve geometric optimization problems on the Cartesian plane.
2
7 lessons
Coordinate Geometry of Circles: Equations, Chords, and Tangents
Analyze circle equations in standard and general forms, determine centers, radii, chord lengths, tangent lines, and intersection properties algebraically.
3
8 lessons
Conic Sections: Geometric Loci and Standard Equations
Understand conics as double-cone cross sections and geometric loci, deriving and graphing standard Cartesian equations of parabolas, ellipses, and hyperbolas.
4
5 lessons
Conics in Polar Coordinates and General Second-Degree Curves
Classify general second-degree quadratic equations via the algebraic discriminant, rotate coordinate axes, and represent conic sections in polar form.
5
7 lessons
Parametric Curves: Conversions and Geometric Trajectories
Model plane curves parametrically, convert between parametric and Cartesian representations, and analyze 2D kinematics, projectile motion, and cycloids.