Hyperbola Exploration Worksheet
Explore the properties and equations of hyperbolas, including their standard forms, vertices, foci, and asymptotes, through various exercises.
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Hyperbola Exploration Worksheet
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Read each question carefully and provide your answers in the spaces provided. Show all your work for full credit.
1. Which of the following is the standard form equation of a hyperbola centered at the origin?
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$
$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$
$$y = ax^2 + bx + c$$
$$(x-h)^2 + (y-k)^2 = r^2$$
2. The two fixed points of a hyperbola are called its .
3. The lines that a hyperbola approaches but never touches are called .
4. Sketch the graph of the hyperbola with the equation $$\frac{x^2}{9} - \frac{y^2}{4} = 1$$. Clearly label the vertices and asymptotes.
5. Determine the vertices and foci of the hyperbola with the equation $$\frac{y^2}{16} - \frac{x^2}{9} = 1$$.
6. The transverse axis of a hyperbola always lies along the x-axis.
True
False