When in standard form find the eccentricity, center, foci and vertices of an ellipse

The video tutorial covers the problem of finding the center, foci, and eccentricity of an ellipse, and how to sketch its graph. It explains the concepts of major and minor axis symmetry, and how to determine them using the values of a^2 and b^2. The tutorial also demonstrates how to calculate the center, foci, and vertices of the ellipse, and how to graph it. Finally, it discusses the concept of eccentricity and its role in determining the shape of the ellipse.

What is the length of the major axis in an ellipse with a major axis symmetry?

• A

• 2A

• 2B

• B

How do you determine if an ellipse has a vertical or horizontal major axis?

• By looking at the eccentricity

• By checking the center coordinates

• By comparing the values of a^2 and b^2

• By comparing the coefficients of x and y

What is the formula for the equation of an ellipse with a vertical major axis?

• (x-h)^2/b^2 - (y-k)^2/a^2 = 1

• (x-h)^2/a^2 - (y-k)^2/b^2 = 1

• (x-h)^2/b^2 + (y-k)^2/a^2 = 1

• (x-h)^2/a^2 + (y-k)^2/b^2 = 1

What are the coordinates of the center of an ellipse?

• H, K

• C, D

• A, B

• X, Y

Which formula is used to find the distance to the foci in an ellipse?

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 = c^2 - b^2

What is the relationship between the center and the foci in a vertical ellipse?

• The foci are randomly placed

• The foci are vertically aligned with the center

• The foci are diagonally aligned with the center

• The foci are horizontally aligned with the center

How do you find the vertices of an ellipse with a vertical major axis?

• H ± B, K

• H, K ± B

• H, K ± A

• H ± A, K

In the context of ellipses, what does the term 'foci' refer to?

• The endpoints of the minor axis

• The center of the ellipse

• Two fixed points inside the ellipse

• The endpoints of the major axis

What is the eccentricity of an ellipse with foci distance 3 and major axis length 5?

• 0.5

• 0.6

• 0.7

• 0.8

What does the eccentricity of an ellipse indicate?

• The size of the ellipse

• The position of the ellipse

• The shape of the ellipse

• The color of the ellipse