Hyperbolas Review

Front

What are the coordinates of the vertices of a vertical hyperbola centered at the origin with a distance of 5 from the center?

Back

(0, 5) and (0, -5)

Front

How can you determine if a hyperbola is vertical or horizontal?

Back

A hyperbola is vertical if its transverse axis is vertical, meaning it opens upwards and downwards.

Front

What is the center of a hyperbola?

Back

The center of a hyperbola is the midpoint between its vertices.

Front

What are the vertices of a hyperbola with center (-4, 0) and distance of 3 from the center?

Back

(-4, 3) and (-4, -3)

Front

What is the standard form of the equation of a vertical hyperbola?

Back

(y - k)²/a² - (x - h)²/b² = 1, where (h, k) is the center.

Front

What is the relationship between the foci and vertices of a hyperbola?

Back

The distance from the center to each focus is greater than the distance from the center to each vertex.

Front

How do you find the foci of a hyperbola?

Back

The foci are located at a distance of c from the center, where c = √(a² + b²).

Front

What does the term 'transverse axis' refer to in a hyperbola?

Back

The transverse axis is the line segment that connects the vertices of the hyperbola.

Front

What is the conjugate axis of a hyperbola?

Back

The conjugate axis is perpendicular to the transverse axis and passes through the center.

Front

What is the significance of the asymptotes in a hyperbola?

Back

Asymptotes are lines that the hyperbola approaches but never touches, guiding the shape of the graph.