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 two types of hyperbolas?

Back

Vertical hyperbola and horizontal hyperbola.

Front

How can you identify a vertical hyperbola?

Back

A vertical hyperbola opens upwards and downwards, and its standard form is (y-k)²/a² - (x-h)²/b² = 1.

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 standard form of a hyperbola?

Back

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

Front

What are the foci of a hyperbola?

Back

The foci are the points located along the transverse axis, outside the vertices, that help define the shape of the hyperbola.

Front

How do you find the distance to the foci from the center of a hyperbola?

Back

The distance to the foci is found using the formula c = √(a² + b²), where 'c' is the distance to the foci, 'a' is the distance to the vertices, and 'b' is related to the distance between the branches.

Front

What is the transverse axis of 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 the line segment perpendicular to the transverse axis at the center of the hyperbola.

Front

What does it mean to sketch the graph of a hyperbola?

Back

Sketching the graph involves plotting the vertices, foci, and asymptotes, and drawing the branches of the hyperbola.