Cartesian Equation of Ellipse

The video tutorial introduces the concept of an ellipse, a type of conic section, and its applications in real life, such as planetary orbits and whispering galleries. It defines an ellipse mathematically, explains its properties, and demonstrates how to construct one using a simple activity. The tutorial covers key terms like focus, directrix, and axes, and derives the Cartesian equation of an ellipse. It also discusses the symmetry and area of an ellipse, comparing it to a circle.

Which of the following is NOT a real-life example of an ellipse?

• The surface of liquid in a tilted glass

• The path of electrons in an atom

• The orbit of planets

• The shape of a square

What is the constant ratio called that determines the shape of a conic section?

• Chord

• Directrix

• Focus

• Eccentricity

How many foci does an ellipse have?

• One

• Two

• Three

• Four

What is the major axis of an ellipse?

• A line segment joining any two points on the ellipse

• The shortest chord passing through the center

• The longest chord passing through the center

• A line segment perpendicular to the minor axis

What happens to an ellipse when its foci coincide?

• It becomes a line

• It becomes a parabola

• It becomes a hyperbola

• It becomes a circle

Which axis is the ellipse symmetric about if its major axis lies on the X-axis?

• Neither X nor Y axes

• Both X and Y axes

• Y-axis only

• X-axis only

What is the line called that passes through the foci of an ellipse?

• Chord

• Minor axis

• Major axis

• Directrix

Which of the following is true about the symmetry of an ellipse?

• It is symmetric about the X-axis only

• It is symmetric about the Y-axis only

• It is not symmetric

• It is symmetric about both the X and Y axes

What is the area of an ellipse with semi-major axis 'a' and semi-minor axis 'b'?

• π * a * b

• π * a^2

• 2 * π * a * b

• π * b^2

If the major and minor axes of an ellipse are equal, what shape does it represent?

• Hyperbola

• Ellipse

• Circle

• Parabola