What are the formulas for vertical and horizontal ellipses conic sections

The video tutorial covers the concepts of horizontal and vertical ellipses, focusing on major and minor axes, vertices, and foci. It explains how to find these elements and the formulas used to calculate ellipse properties. The tutorial also discusses the differences between horizontal and vertical ellipses, emphasizing the importance of understanding the placement of variables in equations. The session concludes with a comparison of formulas for different orientations of ellipses.

What is the primary focus of the initial section of the video?

• Detailed explanation of parabolas

• Introduction and quick review of ellipses

• In-depth discussion on foci

• Complex calculations of axes

What is the length of the major axis in an ellipse?

• B

• 2B

• 2A

• A

How do you find the vertices of a horizontal ellipse?

• H, K ± C

• H, K ± A

• H ± C, K

• H ± A, K

In a vertical ellipse, how does the foci affect the vertex?

• It changes the H value

• It changes both H and K values

• It does not affect the vertex

• It changes the K value

What is the relationship between a², b², and c² in an ellipse?

• a² + c² = b²

• a² = b² - c²

• a² + b² = c²

• a² = b² + c²

Why are both variables squared in the ellipse formula?

• To account for both horizontal and vertical bends

• To eliminate the need for a constant

• To represent a single parabola

• To simplify the equation

In a horizontal ellipse, where is a² placed in the formula?

• Under the Y term

• Under the X term

• Under both X and Y terms

• It is not included in the formula