Hyperbola Exploration Worksheet

Explore the properties and equations of hyperbolas, including their standard forms, vertices, foci, and asymptotes, through various exercises.

Grade 9 Math AlgebraConic SectionsHyperbola

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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.GPE.A.3

Topics

mathalgebraconic sectionshyperbolagrade 9

6 sections · Free to use · Printable

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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

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