# Ch 5: Common Core HS Geometry: Conic Sections

The Common Core State Standards include the core concepts that students are expected to learn at each grade level. This common core high school geometry chapter on conic sections can show you how to derive equations of parabolas, ellipses and hyperbolas.

Standard: Derive the equation of a parabola given a focus and directrix. (CCSS.Math.Content.HSG-GPE.A.2)

Standard: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. (CCSS.Math.Content.HSG-GPE.A.3)

This standard focuses on deriving the equations of various conic sections, including parabolas, ellipses and hyperbolas. In addition to deriving equations, students who understand the standard will be able to find the focus, directrix and definition of various conic shapes.

The lessons in this standard show students how to:

• Find the focus and directrix of a parabola
• Uncover the focus and definition of an ellipse and a hyperbola
• Discover the equation of a parabola from the focus and directrix
• Derive the equation of an ellipse or a hyperbola from the foci

Individuals with mastery of this standard will know how to find the focus and directrix of a parabola, as well as the focus and definition of an ellipse and a hyperbola. They will also be able to find the equation of a parabola, ellipse and hyperbola from the focus.

### How to Use These Lessons in Your Classroom

Below are tips for utilizing these lessons in the classroom to complement instruction in the CCSS.Math.Content.HSG-GPE.A.2 and CCSS.Math.Content.HSG-GPE.A.3 standards:

#### Working with Parabolas Lessons

Assign the chapters The Focus and Directrix of a Parabola and Finding the Equation of a Parabola from the Focus and Directrix for homework. Have students break into small groups and switch off between finding the focus and directrix from a parabola equation and its opposite operation of using the parabola equation to discover the focus and directrix.

#### Using Ellipses and Hyperbolas

Split students into two groups: one that covers ellipses and another group that covers hyperbolas. Have each group answer questions requiring them to derive the equation and find the focus and definition of their respective conic section. After they've answered a few questions, tell the students to switch.

#### Conic Section Practice Lessons

Have students watch the Practice with Conic Sections video lesson and answer all example questions. Go over these practice quiz answers in class.

6 Lessons in Chapter 5: Common Core HS Geometry: Conic Sections
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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