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The family of curves defined by the equation y = k/x represents:
The family of curves defined by the equation y = k/x represents:
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The family of curves defined by the equation y = k/x represents:
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The equation y = k/x represents a family of hyperbolas.
Questions & Step-by-step Solutions
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Q: The family of curves defined by the equation y = k/x represents:
Solution:
The equation y = k/x represents a family of hyperbolas.
Steps: 5
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Step 1: Understand the equation y = k/x. Here, 'k' is a constant number.
Step 2: Recognize that as 'k' changes, the shape of the graph changes, but the general form remains the same.
Step 3: Identify that the graph of y = k/x is not a straight line; it curves.
Step 4: Learn that these curves are called hyperbolas, which are a type of conic section.
Step 5: Conclude that since 'k' can be any number, the equation y = k/x represents a family of hyperbolas.
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