Eccentricity Explained Through Circles and Ellipses

The video explains that the eccentricity of a circle is zero. It begins by introducing the concept of eccentricity and the standard equation of an ellipse. The video then demonstrates how an ellipse transforms into a circle when its semi-major and semi-minor axes are equal, which is when the ellipse's eccentricity becomes zero. The calculation of eccentricity is shown using the formula c^2 = a^2 - b^2, and it is concluded that for a circle, the eccentricity is zero.

What is the eccentricity of a circle?

• One

• Zero

• Infinity

• Undefined

In the standard equation of an ellipse, what does 'a' represent?

• Semi-minor axis

• Semi-major axis

• Radius

• Diameter

What happens to an ellipse when the lengths of its semi-major and semi-minor axes are equal?

• It remains an ellipse

• It becomes a circle

• It becomes a hyperbola

• It becomes a parabola

What is the term used for the length of the semi-major and semi-minor axes when they are equal in a circle?

• Radius

• Tangent

• Diameter

• Chord

What is the expression for the eccentricity of an ellipse?

• c = a - b

• c = a + b

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

If a = b in an ellipse, what does the expression for eccentricity simplify to?

• e^2 = 0

• e^2 = b^2

• e^2 = a^2

• e^2 = 1

Why can't the length of the semi-major axis be zero?

• Because it would make the ellipse a parabola

• Because it would make the ellipse a point

• Because it would make the ellipse a hyperbola

• Because it would make the ellipse a line

What is the relationship between 'c' and the eccentricity 'e' in an ellipse?

• c = a * e

• c = b * e

• c = e / a

• c = e / b