Hyperbolas

Front

What is the equation describing the relationship between dimensions and foci of a hyperbola?

Back

c² = a² + b²

Front

What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1?

Back

(0, ±√17)

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 or (x-h)²/a² - (y-k)²/b² = 1.

Front

What do the variables a, b, and c represent in the context of hyperbolas?

Back

a is the distance from the center to the vertices, b is the distance from the center to the co-vertices, and c is the distance from the center to the foci.

Front

How do you find the foci of a hyperbola given a² and b²?

Back

The foci can be found using the formula c = √(a² + b²).

Front

What is the difference between a hyperbola and an ellipse?

Back

A hyperbola consists of two separate curves, while an ellipse is a closed curve.

Front

What is the transverse axis of a hyperbola?

Back

The transverse axis is the line segment that connects the two 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

How do you graph a hyperbola?

Back

Identify the center, plot the vertices, draw the asymptotes, and sketch the branches.

Front

What are asymptotes in the context of hyperbolas?

Back

Asymptotes are lines that the hyperbola approaches but never touches.