Everything you need to know for conic sections Ellipses

The video tutorial covers unit 9 on vectors, focusing on understanding parabolas and ellipses. It emphasizes the importance of understanding the focus and value of PE in parabolas. The tutorial explains the properties of ellipses, including major and minor axes, and introduces circle and ellipse formulas. It also discusses the orientation of ellipses based on equations and explains the concept of eccentricity.

What is the shape of an ellipse that is not elongated on either axis?

• Oval

• Rectangle

• Triangle

• Circle

Which axis contains the vertices and foci in an ellipse?

• None of the above

• Minor axis

• Diagonal axis

• Major axis

What is the distance from the center to a vertex in an ellipse called?

• d

• a

• c

• b

What is the term for the points on the minor axis of an ellipse?

• Centers

• Vertices

• Foci

• Co-vertices

If an ellipse is elongated vertically, which axis is longer?

• Diagonal axis

• Vertical axis

• Horizontal axis

• None of the above

In the equation of a circle, what does 'r' represent?

• Area

• Circumference

• Diameter

• Radius

Which of the following is true for a circle?

• Only one axis exists

• Major and minor axes are equal

• Axes are perpendicular

• Major axis is longer than minor axis

What is the formula for the equation of a circle centered at (h, k)?

• (x + h)^2 + (y + k)^2 = r^2

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

How are the values of a, b, and c related in an ellipse?

• a^2 + b^2 = c^2

• c^2 = a^2 - b^2

• b^2 = a^2 + c^2

• a^2 = b^2 + c^2

What does the eccentricity of an ellipse measure?

• The area of the ellipse

• The ratio of c to a

• The length of the major axis

• The distance between foci