BetterGrades Precalculus · Unit 13 · Unit map
Conic Sections and Implicit Relations
Find the locus of points exactly 5 units from (-2,3) and determine its x- and y-intercepts.
Precalculus · Unit 13
The lesson path
Find the locus of points exactly 5 units from (-2,3) and determine its x- and y-intercepts.
Core sequence
Conic Sections and Implicit Relations
Move in order when the material is new, or enter at the exact skill you need.
- 01Conics as loci and the circle foundationDefine loci by distance conditions and derive the standard circle equation.
- 02Parabolas from focus and directrixDerive and analyze parabolas as points equidistant from a focus and directrix.
- 03EllipsesAnalyze ellipses from constant-sum distance and standard equations.
- 04HyperbolasAnalyze hyperbolas from constant-difference distance and standard equations.
- 05Completing squares in two variablesConvert general quadratic relations to standard conic form by completing squares.
- 06Translated conics and general equationsClassify translated conics and recover all geometric features from standard form.
- 07Degenerate conics and classificationIdentify point, line, pair-of-lines, empty-set, and other degenerate quadratic relations.
- 08Eccentricity and unified conic structureUse eccentricity to compare circles, ellipses, parabolas, and hyperbolas.
- 09Nonlinear systems involving conicsSolve and interpret intersections of lines, circles, parabolas, ellipses, and hyperbolas.
- 10Conic models and applicationsConstruct and critique conic models in reflection, orbit, architecture, and navigation settings.
References used for this unit
- Lippman & Rasmussen, Precalculus Vol. 2, Chapter 9
- Stitz & Zeager, Precalculus, Chapter 7
- University of Washington Precalculus, conic problem sets
The learner copy is original BetterGrades material informed by these rights-separated references; no long source passage is reproduced.