Hyperbola 1

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section that appears as two separate curves, known as branches, which open away from each other.

Front

What are the foci of a hyperbola?

Back

The foci are two fixed points located along the transverse axis of the hyperbola, which help define its shape.

Front

What are the vertices of a hyperbola?

Back

The vertices are the points where the hyperbola intersects its transverse axis.

Front

What is the center of a hyperbola?

Back

The center is the midpoint between the two foci and is the point where the hyperbola is symmetric.

Front

What are the asymptotes of a hyperbola?

Back

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

Front

How do you find the distance between the foci of a hyperbola?

Back

The distance between the foci is calculated using the formula 2c, where c is the distance from the center to each focus.

Front

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

Back

The standard form is (x-h)²/a² - (y-k)²/b² = 1 for horizontal hyperbolas and (y-k)²/a² - (x-h)²/b² = 1 for vertical hyperbolas.

Front

What does 'transverse axis' mean in a hyperbola?

Back

The transverse axis is the line segment that connects the vertices of the hyperbola and passes through the foci.

Front

What does 'conjugate axis' mean in a hyperbola?

Back

The conjugate axis is the line segment perpendicular to the transverse axis at the center, defining the width of the hyperbola.

Front

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

Back

In a hyperbola, c² = a² + b², where a is the distance from the center to a vertex and b is the distance from the center to a point on the conjugate axis.