what is the characteristics and formula for a horizontal hyperbola

The video tutorial covers the characteristics of hyperbolas, comparing them with ellipses. It explains the concepts of center, vertices, and foci, and introduces the transverse and conjugate axes. The tutorial also discusses asymptotes and provides the formula for the equation of a hyperbola, highlighting the differences from an ellipse.

What is a key difference between the graph of a hyperbola and an ellipse?

• An ellipse's graph focuses away from the center.

• A hyperbola's graph focuses away from the center.

• A hyperbola has a closed shape.

• An ellipse has no vertices.

In a hyperbola, what is the distance from the center to the vertices called?

• Minor axis

• Conjugate axis

• Transverse axis

• Major axis

In the context of hyperbolas, what does the term 'conjugate axis' refer to?

• The distance from the center to the foci

• The axis perpendicular to the transverse axis

• The axis parallel to the transverse axis

• The distance from the center to the vertices

What is the term for the line that a hyperbola approaches but never touches?

• Vertex

• Focus

• Asymptote

• Axis

What is the formula for the asymptotes of a hyperbola?

• y = ± (b/a)(x + h)

• y = ± (a/b)(x + h)

• y = ± (a/b)(x - h)

• y = ± (b/a)(x - h)

How is the equation of a hyperbola different from that of an ellipse?

• The larger number is always under the y-term.

• The equation always has a plus sign.

• The equation always has a minus sign.

• The larger number is always under the x-term.

When determining the equation of a hyperbola, which term is always first?

• The term with 'b' in the denominator

• The term with 'a' in the denominator

• The term with the smaller denominator

• The term with the larger denominator