what is the formula's for the asymptotes of a hyperbola

The video tutorial covers the properties and equations of hyperbolas, focusing on asymptotes and the differences between hyperbolas and ellipses. It explains the formulas for horizontal and vertical asymptotes and how to find 'b' using the equations. The tutorial also compares the equations of ellipses and hyperbolas, highlighting the differences in their mathematical relationships.

What is a key characteristic of hyperbolas that differentiates them from ellipses?

• They have asymptotes.

• They have circular shapes.

• They have directorates.

• They have enclosed systems.

Which formula is used to find the horizontal asymptote of a hyperbola?

• y = h ± a/b (x - k)

• y = h ± b/a (x - k)

• y = k ± b/a (x - h)

• y = k ± a/b (x - h)

How many asymptotes does a hyperbola have?

• Two, one with a positive slope and one with a negative slope

• None

• One with a positive slope

• One with a negative slope

What is the relationship between a, b, and c for a hyperbola?

• a² = b² + c²

• b² = a² + c²

• c² = a² - b²

• a² = c² - b²

For an ellipse, what is the equation relating a, b, and c?

• b² = a² - c²

• a² = c² - b²

• c² = a² + b²

• a² = b² + c²