HSG-GPE.A.3

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- HSG-GPE.A.1Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
- HSG-GPE.A.2Derive the equation of a parabola given a focus and directrix.
- HSG-GPE.A.3Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

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## HSG-GPE.A.3

## 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.

21 Lesson(s)

Big Idea:

#### After learning to write the equation of an ellipse, students design an elliptical pool table that would guarantee that even the worst player can always make a shot.

Standards:

Favorites
(5)

Resources
(19)

### Conics Sections with Princess the Dog

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students will refresh their knowledge of conic sections using an interactive format.

Standards:

Favorites
(1)

Resources
(21)

Reflections
(2)

Big Idea:

#### Through a poster students place wax paper designs made in previous lessons on a graph then determine the equation for the conic represented by the design.

Standards:

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(1)

Resources
(25)

Reflections
(4)

Big Idea:

#### Define an ellipse in three different ways.

Standards:

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(1)

Resources
(12)

Reflections
(1)

Big Idea:

#### How can I put a conic on a coordinate plane so that an equation can be found?

Standards:

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(1)

Resources
(22)

Reflections
(4)

### Rotated Conic Sections - Day 1 of 2

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### y = (1/x) is a hyperbola, but why is its equation so different than other hyperbolas?

Standards:

Favorites
(1)

Resources
(11)

Reflections
(1)

Big Idea:

#### How is an ellipse different than a circle?

Standards:

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(2)

Resources
(17)

Reflections
(1)

Big Idea:

#### How can I determine the equation is an ellipse by looking at the equation.

Standards:

Favorites
(1)

Resources
(26)

Reflections
(2)

Big Idea:

#### How are the definition and standard equation similar to the ellipse's definition and equation?

Standards:

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(1)

Resources
(17)

Big Idea:

#### Students identify and make use of the structure of an equation as they learn to graph hyperbolas.

Standards:

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(3)

Resources
(16)

### Conic Sections Unit Test

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students show their personal knowledge of graphing and writing equations for conic sections.

Standards:

Favorites
(2)

Resources
(4)

Big Idea:

#### Students will fold away to discover the relationship between a focus, directrix and parabola as well as play Jeopardy to review key topics in Line-sanity unit including alternate interior angles.

Standards:

Favorites
(1)

Resources
(22)

Reflections
(2)

### Conic Sections Test Review

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students work together and ask questions as they prepare for tomorrow's unit test.

Standards:

Favorites
(2)

Resources
(4)

### Hashing Out Hyperbolas

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Analyze hyperbolas using three different lenses.

Standards:

Favorites
(1)

Resources
(11)

Reflections
(1)

Big Idea:

#### The game show Lingo inspires this conic section review.

Standards:

Favorites
(2)

Resources
(6)

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