Conics What are the important parts of a horizontal ellipse

The video tutorial reviews conic sections, focusing on parabolas, circles, and ellipses. It explains the properties of parabolas, including the vertex, focus, and directrix. The tutorial then covers circles, highlighting the center and radius. The main focus is on ellipses, discussing their structure, including the center, vertices, co-vertices, major and minor axes, and foci. The video also explains the equations for circles and ellipses, emphasizing the differences in their mathematical representations.

What is the definition of a parabola in terms of its focus and directrix?

• A parabola is the set of all points equidistant from a point called the focus and a line called the directrix.

• A parabola is the set of all points equidistant from a line called the axis.

• A parabola is the set of all points equidistant from two points called foci.

• A parabola is the set of all points equidistant from a center point.

How does an ellipse differ from a circle?

• An ellipse has a constant radius like a circle.

• An ellipse is elongated in one direction, unlike a circle.

• An ellipse has only one focus, while a circle has two.

• An ellipse has no center, unlike a circle.

What are the major and minor axes in an ellipse?

• Both axes are equal in length in an ellipse.

• The major axis is the longer distance across the ellipse, and the minor axis is the shorter distance.

• The major axis is vertical, and the minor axis is horizontal.

• The major axis is the shorter distance across the ellipse, and the minor axis is the longer distance.

How is the equation of a circle transformed to have a right-hand side of 1?

• By dividing the entire equation by the radius.

• By multiplying the entire equation by the radius squared.

• By dividing the entire equation by the radius squared.

• By adding the radius squared to both sides.

In the equation of an ellipse with a horizontal axis, what does 'a' represent?

• The distance from the center to the co-vertex.

• The distance from the center to the directrix.

• The distance from the center to the vertex.

• The distance from the center to the focus.

What is the relationship between a, b, and c in an ellipse?

• a^2 = c^2 - b^2

• a^2 = b^2 + c^2

• a^2 = b^2 - c^2

• a^2 = b^2 * c^2

Which of the following best describes the relationship of a, b, and c in an ellipse?

• It is similar to the Pythagorean theorem.

• It is unrelated to the Pythagorean theorem.

• It is the same as the Pythagorean theorem.

• It contradicts the Pythagorean theorem.