Math Problem Statement
,b, and c. ((x^2)/4)-(y^2)=1
Solution
The equation you've provided resembles a hyperbola. Let's rewrite and analyze the equation:
Analysis
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Standard Form: The equation of a hyperbola in standard form is given by:
In this form, is associated with the -term, and with the -term if the hyperbola opens left-right, or vice versa if it opens up-down.
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Identification of and : Comparing your equation with the standard form:
- so
- so
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Characteristics:
- The hyperbola opens left-right because the -term is positive.
- The transverse axis length is .
- The conjugate axis length is .
- The center of the hyperbola is at the origin .
Related Questions
- What is the length of the transverse axis?
- How would the equation change if the hyperbola opened up-down?
- Can you find the equations of the asymptotes for this hyperbola?
- What are the coordinates of the vertices of the hyperbola?
- How would the equation change if the center of the hyperbola were at ?
- How do you find the foci of this hyperbola?
- Can you sketch the graph of this hyperbola?
- How does the equation change if the hyperbola is rotated?
Tip
To determine the orientation of a hyperbola, check the signs in the standard form equation. If the -term is positive, the hyperbola opens horizontally; if the -term is positive, it opens vertically.
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Math Problem Analysis
Mathematical Concepts
Hyperbola
Conic Sections
Formulas
Standard form of a hyperbola
Theorems
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Suitable Grade Level
Advanced High School