Conic Sections and Their Properties

The video tutorial explains how to graph polar equations of conic sections, including ellipses, parabolas, and hyperbolas. It covers the forms of polar equations, how to determine eccentricity, and provides examples of graphing each type of conic section. The tutorial also discusses how to convert polar equations to rectangular form and calculate key parameters like the length of axes and the position of the directrix.

What is the eccentricity of a conic section if it is a parabola?

• 0

• Less than 1

• Greater than 1

• 1

Which direction does a conic section open if the equation is r = e*d / (1 + e*sin(theta))?

• Downward

• Upward

• Left

• Right

In the equation r = 6 / (2 - cos(theta)), what type of conic section is represented if e = 0.5?

• Parabola

• Ellipse

• Circle

• Hyperbola

How do you determine the length of the major axis of an ellipse?

• 2a

• a + b

• 2b

• a - b

For the equation r = 4 / (1 + cos(theta)), what is the conic section if e = 1?

• Parabola

• Ellipse

• Circle

• Hyperbola

What is the rectangular form of an ellipse with center (2, 0), a = 4, and b = 2√3?

• (x-2)^2/16 + y^2/12 = 1

• (x+2)^2/16 + y^2/12 = 1

• (x-2)^2/12 + y^2/16 = 1

• (x+2)^2/12 + y^2/16 = 1

What is the value of d if the directrix is y = 7 and e = 5/4?

• 7

• 5

• 3

• 4

If a parabola has a vertex at (2, pi), what is the equation of the directrix?

• x = -4

• y = 4

• x = 4

• y = -4

What is the standard form of a hyperbola that opens up and down?

• x^2/b^2 - y^2/a^2 = 1

• x^2/a^2 - y^2/b^2 = 1

• y^2/a^2 - x^2/b^2 = 1

• y^2/b^2 - x^2/a^2 = 1

How do you find the center of a hyperbola given its vertices?

• Average of x-coordinates

• Average of y-coordinates

• Sum of vertices

• Midpoint of vertices