What is the family of curves represented by the equation xy = c?

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Question: What is the family of curves represented by the equation xy = c?

Options:

Correct Answer: Hyperbolas

Solution:

The equation xy = c represents a family of hyperbolas with varying constant c.

What is the family of curves represented by the equation xy = c?

What is the family of curves represented by the equation xy = c?

Step 1: Understand the equation xy = c. Here, x and y are variables, and c is a constant number.
Step 2: Recognize that this equation can be rearranged to y = c/x. This shows how y changes based on the value of x.
Step 3: Identify that as c changes (for different values of c), the shape of the graph changes, but the general form remains the same.
Step 4: Realize that the graph of y = c/x is a hyperbola, which is a specific type of curve.
Step 5: Conclude that the equation xy = c represents a family of hyperbolas, where each hyperbola corresponds to a different value of c.

No concepts available.