Question: If the family of curves is given by y = k/x, what type of curves does it represent?
Options:
Linear
Hyperbolic
Circular
Exponential
Correct Answer: Hyperbolic
Solution:
The equation y = k/x represents a family of hyperbolas.
If the family of curves is given by y = k/x, what type of curves does it represe
Practice Questions
Q1
If the family of curves is given by y = k/x, what type of curves does it represent?
Linear
Hyperbolic
Circular
Exponential
Questions & Step-by-Step Solutions
If the family of curves is given by y = k/x, what type of curves does it represent?
Step 1: Identify the equation given, which is y = k/x.
Step 2: Recognize that 'k' is a constant that can take different values.
Step 3: Understand that for different values of 'k', the shape of the curve changes but follows the same general form.
Step 4: Recall that the equation y = k/x is a standard form of a hyperbola.
Step 5: Conclude that as 'k' varies, the curves represent different hyperbolas.
Hyperbolas – The equation y = k/x represents a family of hyperbolas, which are defined as the set of points where the product of the distances to two fixed points (foci) is constant.
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