Lesson : 9.4 -Polar Forms of Conic Sections

Multiple Choice

What is the significance of studying polar forms of conic sections in mathematics?

• They help us understand planetary orbits and navigation.

• They are only used in art and design.

• They are not relevant to real-world applications.

• They are mainly used for solving basic algebra problems.

Multiple Choice

Which point represents (5, π)

• F
• E
• B
• A

Multiple Choice

What is the function of the graph?

• r=3
• r=3sinΘ
• r=3sinΘ+3cosΘ
• r=3cosΘ

Multiple Choice

Which vocabulary term describes the line used to define conic sections in polar equations?

• Conic Section

• Directrix

• Eccentricity

• Focus

Multiple Choice

Which equation represents the polar graph?

• r = sin θ
• r = sin 4θ
• r = 4 sin θ
• r = 4 cos θ

Multiple Choice

Find the ordered pair for the focus of the conic pictured.

• (5, 4)
• (3, 6)
• (1, 4)
• (3, 2)

Multiple Choice

Which conic section is represented by the polar equation r = 12/(1+3cosθ)?

• Parabola

• Ellipse

• Hyperbola

• Circle

Open Ended

Explain how eccentricity determines the classification of a conic section as an ellipse, parabola, or hyperbola.

Open Ended

Describe the relationship between the focus, directrix, and eccentricity for an ellipse, parabola, and hyperbola.

Multiple Select

Select all equations that represent a parabola in polar form.

• r = 12/(1+3cosθ)

• r = ed/(1+e cosθ) with e=1

• r = 10/(5-2sinθ)

• r = ed/(1-e sinθ) with e=1

Multiple Choice

The eccentricity of a parabola is/could be _____.

• 0
• 0.5
• 1
• 5

Open Ended

Compare the process of finding the eccentricity and directrix for the equations r = 10 / (3 + 2cosθ) and r = -15 / (6sinθ - 3). What are the key similarities and differences?

Multiple Choice

Determine the eccentricity, type of conic, and equation of the directrix for r = 12/(4 + 2sinθ).

• e = 0.5; ellipse; y = 12

• e = 1; parabola; x = 6

• e = 2; hyperbola; x = -6

• e = 0.5; ellipse; y = 6

Multiple Choice

Which conic section is represented by the polar equation r = 12/(1 + 3cosθ)?

• Parabola

• Ellipse

• Hyperbola

• Circle

Multiple Choice

In the equation r = 15/(3 - 9sinθ), what is the eccentricity (e) and the resulting shape?

• e = 9; Hyperbola

• e = 3; Hyperbola

• e = 5; Ellipse

• e = 15; Parabola

Open Ended

What are the key classroom rules students should follow according to the lesson?

Open Ended

Explain how the polar equation of a conic section changes when the directrix is vertical versus horizontal.

Multiple Choice

A parabola (e = 1) has a directrix at x = -3. What is the value of the numerator (ed) in its polar equation?

• 1

• -3

• 3

• 0

Multiple Choice

If a conic has a horizontal directrix at y = 5, which trigonometric function must appear in the denominator of its polar equation?

• cosθ

• sinθ

• tanθ

• secθ

Open Ended

What is one thing you learned today about polar forms of conic sections?