Hyperbola

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section that appears as two separate curves, defined as the set of all points where the difference of the distances to two fixed points (foci) is constant.

Front

What is the standard equation of a hyperbola centered at the origin?

Back

The standard equation is (x^2/a^2) - (y^2/b^2) = 1 for a horizontal hyperbola and (y^2/a^2) - (x^2/b^2) = 1 for a vertical hyperbola.

Front

What do 'a' and 'b' represent in the context of a hyperbola?

Back

'a' represents the distance from the center to the vertices, while 'b' represents the distance from the center to the co-vertices.

Front

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

Back

The relationship is given by the equation c^2 = a^2 + b^2, where 'c' is the distance from the center to the foci.

Front

What is the length of the transverse axis of a hyperbola?

Back

The length of the transverse axis is 2a.

Front

What is the length of the conjugate axis of a hyperbola?

Back

The length of the conjugate axis is 2b.

Front

How do you find the foci of a hyperbola?

Back

The foci are located at (±c, 0) for a horizontal hyperbola and (0, ±c) for a vertical hyperbola, where c = √(a^2 + b^2).

Front

What is the asymptote equation for a horizontal hyperbola?

Back

The asymptotes are given by y = ±(b/a)x.

Front

What is the asymptote equation for a vertical hyperbola?

Back

The asymptotes are given by y = ±(a/b)x.

Front

What is the significance of the foci in a hyperbola?

Back

The foci are important because they define the hyperbola and are used to determine its shape and dimensions.