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Determine the family of curves represented by the equation y = k/x, where k is a
Determine the family of curves represented by the equation y = k/x, where k is a constant.
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Practice Questions
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Q1
Determine the family of curves represented by the equation y = k/x, where k is a constant.
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The equation y = k/x represents a family of hyperbolas with varying values of 'k'.
Questions & Step-by-step Solutions
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Q: Determine the family of curves represented by the equation y = k/x, where k is a constant.
Solution:
The equation y = k/x represents a family of hyperbolas with varying values of 'k'.
Steps: 5
Show Steps
Step 1: Understand the equation y = k/x. Here, 'y' is the output, 'k' is a constant, and 'x' is the input.
Step 2: Recognize that 'k' can take any value (positive, negative, or zero), which will change the shape of the curve.
Step 3: Rewrite the equation in a different form: y * x = k. This shows that the product of 'y' and 'x' is constant (equal to 'k').
Step 4: Identify that as 'k' changes, the curves will shift and stretch, but they will all have a similar shape, which is a hyperbola.
Step 5: Conclude that the equation y = k/x represents a family of hyperbolas, each corresponding to a different value of 'k'.
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