How many foci does the graph of a hyperbola have?A.1B.3C.2D.0SUBMITarrow_backPREVIOUS
Question
How many foci does the graph of a hyperbola have?
A. 1
B. 3
C. 2
D. 0
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Solution
Understanding the Hyperbola
A hyperbola is a type of conic section that is defined mathematically and has distinct characteristics.
Foci of a Hyperbola
- Definition of Foci: A hyperbola has two distinct focal points (foci), which are essential for its definition.
- Geometric Significance: The foci are located along the transverse axis, and they help determine the shape and orientation of the hyperbola.
Options Analysis
- A. 1: Incorrect; a hyperbola must have two foci.
- B. 3: Incorrect; there's no conic section with three foci.
- C. 2: Correct; a hyperbola has exactly two foci.
- D. 0: Incorrect; a hyperbola cannot exist without foci.
Conclusion
By analyzing the properties of a hyperbola, we can conclude that it has 2 foci.
Final Answer
C. 2
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