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A hyperbola centered at the origin has a squared equal to 64 and b squared equal to 36. How far is each focus from the center?
ASix units from the center
BTen units from the center
CEight units from the center
DFourteen units from the center
Answer & Solution
Correct answer: B. Ten units from the center
1. For a hyperbola, c squared equals a squared plus b squared, a sum rather than a difference.
2. Adding gives 64 plus 36, which is 100.
3. Taking the square root gives c equal to 10 units.
4. Answering 8 units uses a alone and ignores the b squared term entirely.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_
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