Conic Sections and Polar Coordinates

The video tutorial covers conic sections and their representation in polar coordinates. It explains the properties of conic sections, including ellipses, parabolas, and hyperbolas, based on eccentricity. The tutorial derives equations for conics in polar form and provides examples of finding polar equations for specific conics. It also demonstrates how to sketch conic sections, identify key features like vertices and asymptotes, and rotate conics in polar coordinates. Finally, the video discusses elliptical orbits, focusing on calculating perihelion and aphelion distances.

What is the fixed point in a conic section called?

• Eccentricity

• Directrix

• Focus

• Vertex

If the eccentricity of a conic section is less than one, what type of conic is it?

• Parabola

• Circle

• Ellipse

• Hyperbola

What is the polar equation for a conic section with a focus at the origin?

• r = ed/(1 ± e cos θ)

• r = e/(1 ± d cos θ)

• r = d/e

• r = e/d

How do you convert a polar equation to rectangular coordinates?

• Use r^2 = x^2 + y^2

• Use r = x + y

• Use r = x^2 - y^2

• Use r = x/y

What is the purpose of completing the square in conic sections?

• To find the focus

• To find the directrix

• To find the eccentricity

• To convert to standard form

In the example of a parabola with focus at the origin, what is the directrix?

• x = -6

• x = 6

• y = -6

• y = 6

What is the eccentricity of the conic given by r = 10/(3 - 2 cos θ)?

• 1

• 2/3

• 1/3

• 3/2

How can conics be rotated in polar coordinates?

• By multiplying r by a constant

• By subtracting a constant from θ

• By adding a constant to r

• By dividing θ by a constant

What is the approximate polar equation for Earth's orbit around the sun?

• r = 1.495 × 10^8/(1 - 0.017 cos θ)

• r = 1.495 × 10^8/(1 + 0.017 sin θ)

• r = 1.495 × 10^8/(1 + 0.017 cos θ)

• r = 1.495 × 10^8/(1 - 0.017 sin θ)