Graphing Conic Sections Part 4: Hyperbolas

The video tutorial covers hyperbolas, the last conic section, explaining their definition, properties, and equations. It compares hyperbolas to ellipses, highlighting the differences in foci and the constant difference in distances. The tutorial provides an example of a hyperbola equation, demonstrates sketching techniques, and discusses asymptotes and transformations. Key concepts include the transverse axis, vertices, and the role of a, b, and c terms in the equation.

What is the main difference between the distances to the foci in a hyperbola compared to an ellipse?

• In a hyperbola, the distances have a constant sum.

• In a hyperbola, the distances have a constant difference.

• In an ellipse, the distances have a constant product.

• In an ellipse, the distances have a constant difference.

How does the equation of a hyperbola differ from that of an ellipse?

• The hyperbola equation has a minus sign instead of a plus.

• The hyperbola equation has a plus sign instead of a minus.

• The hyperbola equation has a multiplication sign instead of a division.

• The hyperbola equation has a division sign instead of a multiplication.

In the example problem, if a squared is 16 and b squared is 9, what is the value of c?

• 3

• 6

• 4

• 5

What happens to the transverse axis if the x and y terms in a hyperbola equation are reversed?

• The transverse axis becomes vertical.

• The transverse axis becomes horizontal.

• The transverse axis remains unchanged.

• The transverse axis disappears.

What is the role of asymptotes in drawing hyperbolas?

• They are the lines that the branches of the hyperbola approach but never touch.

• They are the lines that determine the length of the transverse axis.

• They are the lines that the branches of the hyperbola intersect.

• They are the lines that define the center of the hyperbola.

For a hyperbola that opens around the x-axis, what is the equation of the asymptotes?

• y = b * x and y = -b * x

• y = a/b * x and y = -a/b * x

• y = a * x and y = -a * x

• y = b/a * x and y = -b/a * x

How can hyperbolas be transformed similarly to ellipses?

• By rewriting as x / h and y / k.

• By rewriting as x * h and y * k.

• By rewriting as x - h and y - k.

• By rewriting as x + h and y + k.