Understanding how to find the foci and vertices of an ellipse conic sections

The video tutorial covers the properties of a horizontal ellipse, including its major and minor axes, vertices, and foci. The instructor explains how to calculate distances using the Pythagorean theorem and emphasizes the formula a² = c² + b². The lesson aims to clarify the relationships between the ellipse's components and how to apply these concepts in geometry.

What is the major axis in a horizontal ellipse?

• The line that is perpendicular to the minor axis

• The line that stretches vertically

• The line that stretches horizontally

• The line that connects the foci

How are the foci of a horizontal ellipse labeled?

• (h ± a, k)

• (h ± c, k)

• (h, k ± a)

• (h, k ± c)

What is the correct formula for the vertices of a horizontal ellipse?

• (h, k ± a)

• (h ± a, k)

• (h ± c, k)

• (h, k ± c)

What is the definition of an ellipse in terms of its foci?

• The distance from one focus to any point is constant

• The sum of the distances from the foci to any point on the ellipse is constant

• The difference of the distances from the foci to any point on the ellipse is constant

• The product of the distances from the foci to any point on the ellipse is constant

How is the Pythagorean theorem applied to find the relationship between a, b, and c in an ellipse?

• a² = c² - b²

• a² = c² + b²

• a² = b² + c²

• a² = b² - c²

What does 'a' represent in the context of a horizontal ellipse?

• The distance from the center to a focus

• The distance of the minor axis

• The distance between the foci

• Half the distance of the major axis

In a horizontal ellipse, what is the relationship between the total length of the major axis and 'a'?

• The total length is 4a

• The total length is 2a

• The total length is a/2

• The total length is a