Converting to standard form to find the foci, vertices and center of an ellipse

The video tutorial explains how to determine the foci, vertices, and center of an ellipse from its equation. It covers the process of completing the square to transform the equation into standard form, identifies the properties of the ellipse, and calculates its eccentricity. The tutorial emphasizes the differences between horizontal and vertical ellipses and the significance of the major and minor axes.

What are the two possible orientations for the major axis of an ellipse?

• Horizontal and diagonal

• Vertical and diagonal

• Horizontal and vertical

• Diagonal and circular

What is the first step in completing the square for the equation of an ellipse?

• Subtract a constant from both sides

• Multiply both sides by a constant

• Factor out the coefficient of the quadratic term

• Add a constant to both sides

When completing the square, what do you do after factoring out the coefficient?

• Multiply the linear coefficient by two

• Subtract the square of half the linear coefficient

• Divide the linear coefficient by two

• Add the square of half the linear coefficient

How do you determine if an ellipse is vertical or horizontal?

• By checking if the larger numerator is under the x-term

• By checking if the larger numerator is under the y-term

• By checking if the larger denominator is under the y-term

• By checking if the larger denominator is under the x-term

What is the relationship between the center and the vertices of an ellipse?

• They are on the same minor axis

• They are on the same major axis

• They are equidistant from the foci

• They are at the endpoints of the minor axis

How do you find the foci of an ellipse?

• By adding and subtracting the value of b from the center

• By adding and subtracting the value of a from the center

• By adding and subtracting the value of d from the center

• By adding and subtracting the value of c from the center

Which of the following is true about the relationship between a, b, and c in an ellipse?

• a^2 = b^2 + c^2

• b^2 = a^2 + c^2

• c^2 = a^2 + b^2

• a^2 + b^2 = c^2

What is the formula to find the eccentricity of an ellipse?

• c/a

• a/c

• b/a

• a/b

What does an eccentricity value closer to 1 indicate about the shape of an ellipse?

• It is a straight line

• It is more circular

• It is more elongated

• It is a perfect circle

What happens to the ellipse as the eccentricity approaches 0?

• It becomes more circular

• It becomes more elongated

• It becomes a straight line

• It becomes a parabola