MAFS.912.G-GPE.1.3

Derive the equations of ellipses and hyperbolas given the foci and directrices.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Translate between the geometric description and the equation for a conic section. (Geometry - Additional Cluster) (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1298310: Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plan

Ellipse Elements and Equations:

Students use both graphic and analytic methods to write the equation of an ellipse given foci and directrices.

Type: Lesson Plan

Perspectives Video: Expert

Sonification and Eccentricity of the Sun:

You may know that you need to use your brain to do science, but did you know you need your ears, too?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Virtual Manipulative

Cool Tool For Ellipses:

Use this interactive GeoGebraTube tool to see how the foci and other graph characteristics are related to the equation of the ellipse.  Make sure you use the sliders to change the characteristics of your ellipse and pay attention to how the graph relates to its equation each time.

Type: Virtual Manipulative

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Virtual Manipulative

Cool Tool For Ellipses:

Use this interactive GeoGebraTube tool to see how the foci and other graph characteristics are related to the equation of the ellipse.  Make sure you use the sliders to change the characteristics of your ellipse and pay attention to how the graph relates to its equation each time.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.