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Exploring Conic Sections Unit 10 Lesson 1

Exploring Conic Sections - · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

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Page 1: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

Exploring Conic Sections

Unit 10 Lesson 1

Page 2: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

EXPLORING CONIC SECTONS

Students will be able to:

Identify different conic sections based on their shapes and general equations.

Key Vocabulary:

• Conic section

• Circle

• Ellipse

• Parabola

• Hyperbola

Page 3: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

A Conic Section is a curve formed by the intersection of a plane anda double cone.

By the intersection of this plane and the conic section, we can have

a circle, an ellipse, a parabola or a hyperbola.

EXPLORING CONIC SECTONS

IntersectionPlane Conic Section

Page 4: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

A Circle is a curve formed by the intersection of a plane and adouble cone such that the plane is perpendicular to the axis of cone.

General equation:

(𝒉, 𝒌) is the center of the circle.

EXPLORING CONIC SECTONS

Circle

(𝒙 − 𝒉)𝟐+(𝒚 − 𝒌)𝟐= 𝒓𝟐

Page 5: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

An Ellipse is a curve formed by the intersection of a plane and adouble cone such that the plane cuts the cone at an angle.

General equations:

(Horizontal Ellipse)

(Vertical Ellipse)

EXPLORING CONIC SECTONS

Ellipse

(𝒙 − 𝒉)𝟐

𝒂𝟐+(𝒚 − 𝒌)𝟐

𝒃𝟐= 𝟏

(𝒙 − 𝒉)𝟐

𝒃𝟐+(𝒚 − 𝒌)𝟐

𝒂𝟐= 𝟏

Page 6: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

A Parabola is a curve formed when the plane cuts any one portion ofthe double cone at angle.

General equations:

(Horizontal parabola)

(Vertical parabola)

𝒂 is the distance from the vertex to the focus.

EXPLORING CONIC SECTONS

Parabola

(𝒚 − 𝒌)𝟐= 𝟒𝒂 𝒙 − 𝒉

(𝒙 − 𝒉)𝟐= 𝟒𝒂 𝒚 − 𝒌

Page 7: Exploring Conic Sections -   · PDF fileExploring Conic Sections ... a circle, an ellipse, a parabola or a hyperbola. ... (Vertical parabola) EXPLORING CONIC SECTONS Hyperbola

A Hyperbola is a curve formed when the plane is parallel to the axisof the double cone and cuts both cones.

General equations:

(Horizontal parabola)

(Vertical parabola)

EXPLORING CONIC SECTONS

Hyperbola

(𝒙 − 𝒉)𝟐

𝒂𝟐−(𝒚 − 𝒌)𝟐

𝒃𝟐= 𝟏

(𝒚−𝒌)𝟐

𝒂𝟐−

(𝒙−𝒉)𝟐

𝒃𝟐= 𝟏