In Class: Hyperbolas Practice

Front

What are the coordinates of the vertices of a hyperbola?

Back

The coordinates of the vertices of a hyperbola are the points where the hyperbola intersects its transverse axis. For example, for the hyperbola with vertices at (-15, 2) and (9, 2), these points are the closest points to the center along the transverse axis.

Front

What is the value of 'b' in the context of hyperbolas?

Back

In hyperbolas, 'b' represents the distance from the center to the co-vertices along the conjugate axis. It is a key parameter in the standard form of the hyperbola's equation.

Front

How do you find the center of a hyperbola?

Back

The center of a hyperbola is the midpoint between its vertices. It can be found by averaging the x-coordinates and y-coordinates of the vertices.

Front

What does the 'c' value represent in a hyperbola?

Back

The 'c' value in a hyperbola represents the distance from the center to the foci. It is calculated using the formula c = √(a² + b²), where 'a' is the distance to the vertices and 'b' is the distance to the co-vertices.

Front

What is the standard form of a hyperbola's equation?

Back

Front

How do you determine the vertices of a hyperbola from its equation?

Back

To find the vertices of a hyperbola from its equation, identify 'a' in the standard form. The vertices are located at (h ± a, k) for horizontal hyperbolas and (h, k ± a) for vertical hyperbolas.

Front

What is the relationship between 'a', 'b', and 'c' in hyperbolas?

Back

In hyperbolas, the relationship is given by the equation c² = a² + b², where 'c' is the distance to the foci, 'a' is the distance to the vertices, and 'b' is the distance to the co-vertices.

Front

How do you graph a hyperbola?

Back

To graph a hyperbola, first plot the center, then plot the vertices and co-vertices. Draw the asymptotes, which guide the shape of the hyperbola, and sketch the curves approaching the asymptotes.

Front

What are asymptotes in the context of hyperbolas?

Back

Asymptotes are lines that the hyperbola approaches but never touches. They provide a guide for the shape of the hyperbola and are found using the equations y = k ± (b/a)(x - h) for horizontal hyperbolas and x = h ± (a/b)(y - k) for vertical hyperbolas.

Front

What is the significance of the transverse and conjugate axes in hyperbolas?

Back

The transverse axis is the line segment that connects the vertices of the hyperbola, while the conjugate axis is perpendicular to the transverse axis and connects the co-vertices. These axes help define the shape and orientation of the hyperbola.