Hyperbolas: Properties and Equations
Explore the properties, equations, and graphing of hyperbolas with this Grade 11 math worksheet.
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Hyperbolas: Properties and Equations
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Read each question carefully and provide your answer in the space 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, with a horizontal transverse axis?
x²/a² + y²/b² = 1
x²/a² - y²/b² = 1
y²/a² - x²/b² = 1
y²/a² + x²/b² = 1
2. The foci of a hyperbola are located at (-5, 0) and (5, 0). If the transverse axis has a length of 8, what is the equation of the hyperbola?
x²/16 - y²/9 = 1
x²/9 - y²/16 = 1
x²/16 - y²/25 = 1
x²/25 - y²/16 = 1
3. The two separate curves of a hyperbola are called .
4. The distance from the center to each focus of a hyperbola is denoted by .
5. Consider the hyperbola with the equation (x-2)²/9 - (y+1)²/16 = 1. Identify the center, vertices, and foci of this hyperbola.
6. Graph the hyperbola given by the equation y²/4 - x²/9 = 1. Clearly label the center, vertices, foci, and asymptotes.