Conic Sections and Eccentricity

This tutorial covers conic sections in polar coordinates, focusing on eccentricity and its role in identifying conic types such as parabolas, ellipses, and hyperbolas. It explains the polar equations for these conics and provides examples of graphing them. The tutorial also demonstrates how to convert conic equations from polar to rectangular form.

What is the term used to describe the ratio of two distances in conic sections?

• Eccentricity

• Symmetry

• Focus

• Directrix

Which conic section has an eccentricity equal to 1?

• Ellipse

• Parabola

• Circle

• Hyperbola

What does an eccentricity greater than 1 indicate?

• Circle

• Ellipse

• Hyperbola

• Parabola

In polar coordinates, what does a cosine in the denominator indicate about the directrix?

• Diagonal line

• Horizontal line

• Vertical line

• No line

If a conic section's equation has a sine in the denominator, what is the orientation of its major axis?

• Diagonal

• Vertical

• Horizontal

• None

What is the eccentricity of a parabola in polar coordinates?

• 0

• 1

• Between 0 and 1

• Greater than 1

For a hyperbola in polar coordinates, what is the typical range of eccentricity?

• 1

• 0

• Greater than 1

• Between 0 and 1

What is the major axis direction for an ellipse with a sine term in its equation?

• None

• Horizontal

• Vertical

• Diagonal

When converting polar equations to rectangular coordinates, what is the relationship between R and x, y?

• R = x * y

• R = sqrt(x^2 + y^2)

• R = x - y

• R = x + y

What is the standard form of a hyperbola in rectangular coordinates derived from polar coordinates?

• x^2 - y^2 = -1

• x^2 + y^2 = 1

• x^2 + y^2 = -1

• x^2 - y^2 = 1