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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 or enter at the exact skill you need.

  1. 01Conics as loci and the circle foundationDefine loci by distance conditions and derive the standard circle equation.
  2. 02Parabolas from focus and directrixDerive and analyze parabolas as points equidistant from a focus and directrix.
  3. 03EllipsesAnalyze ellipses from constant-sum distance and standard equations.
  4. 04HyperbolasAnalyze hyperbolas from constant-difference distance and standard equations.
  5. 05Completing squares in two variablesConvert general quadratic relations to standard conic form by completing squares.
  6. 06Translated conics and general equationsClassify translated conics and recover all geometric features from standard form.
  7. 07Degenerate conics and classificationIdentify point, line, pair-of-lines, empty-set, and other degenerate quadratic relations.
  8. 08Eccentricity and unified conic structureUse eccentricity to compare circles, ellipses, parabolas, and hyperbolas.
  9. 09Nonlinear systems involving conicsSolve and interpret intersections of lines, circles, parabolas, ellipses, and hyperbolas.
  10. 10Conic models and applicationsConstruct and critique conic models in reflection, orbit, architecture, and navigation settings.
Assessment path

Review, practice, demonstrate, investigate

Source record

References used for this unit

  • Lippman & Rasmussen, Precalculus Vol. 2, Chapter 9
  • Stitz & Zeager, Precalculus, Chapter 7
  • University of Washington Precalculus, conic problem sets