The family of curves defined by the equation y = k/x represents:

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Question: The family of curves defined by the equation y = k/x represents:

Options:

Correct Answer: Hyperbolas

Solution:

The equation y = k/x represents a family of hyperbolas.

The family of curves defined by the equation y = k/x represents:

The family of curves defined by the equation y = k/x represents:

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.

Hyperbolas – The equation y = k/x represents a family of hyperbolas, where k is a constant that determines the specific curve.
Inverse Variation – The relationship between x and y in the equation indicates that as one variable increases, the other decreases, demonstrating inverse variation.