Comparing hyperbolas to ellipse's

The video tutorial covers the concepts of ellipses and hyperbolas, focusing on their key characteristics, formulas, and graphing techniques. It explains the differences between ellipses and hyperbolas, including the placement of foci and the use of asymptotes in hyperbolas. The tutorial provides detailed instructions on identifying major and minor axes, vertices, and using specific formulas for graphing and solving problems related to these conic sections.

What is the main difference between the major and minor axes in an ellipse?

• The major axis is always horizontal.

• The minor axis is longer than the major axis.

• The major axis is always vertical.

• The major axis is longer than the minor axis.

In an ellipse, what does the distance 'a' represent?

• Distance from the center to the minor axis

• Distance from the center to the co-vertices

• Distance from the center to the vertices

• Distance from the center to the foci

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

• By checking if b is greater than a

• By checking if b is under the y-term

• By checking if a is greater than b

• By checking if a is under the x-term

What is a key characteristic of hyperbolas compared to ellipses?

• The major axis is always horizontal.

• The foci are outside the vertices.

• The foci are inside the vertices.

• The minor axis is always vertical.

What is the transverse axis in a hyperbola?

• The axis that is always vertical

• The axis that is always horizontal

• The axis that determines the direction of opening

• The axis that is longer than the conjugate axis

How do you identify a hyperbola from its equation?

• By checking if a is greater than b

• By checking if the terms are subtracted

• By checking if b is greater than a

• By checking if the terms are added

What formula is used to find the asymptotes of a hyperbola?

• y = h ± b/a * (x - k)

• y = k ± a/b * (x - h)

• y = k ± b/a * (x - h)

• y = h ± a/b * (x - k)

What role does 'b' play in graphing hyperbolas?

• It determines the length of the conjugate axis.

• It is used to graph the asymptotes.

• It determines the length of the transverse axis.

• It helps in plotting the vertices.

How do you create the box used to graph asymptotes in hyperbolas?

• By using the values of b and c

• By using the values of a and c

• By using the values of a and b

• By using the values of a, b, and c

What is the main difference in the formulas for ellipses and hyperbolas?

• Ellipses use subtraction, hyperbolas use addition

• Ellipses use division, hyperbolas use multiplication

• Ellipses use addition, hyperbolas use subtraction

• Ellipses use multiplication, hyperbolas use division