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The family of curves represented by y^2 = 4ax is known as:

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Question: The family of curves represented by y^2 = 4ax is known as:

Options:

  1. Parabolas
  2. Ellipses
  3. Hyperbolas
  4. Circles

Correct Answer: Parabolas

Solution: 

The equation y^2 = 4ax represents a family of parabolas.

The family of curves represented by y^2 = 4ax is known as:

Practice Questions

Q1
The family of curves represented by y^2 = 4ax is known as:
  1. Parabolas
  2. Ellipses
  3. Hyperbolas
  4. Circles

Questions & Step-by-Step Solutions

The family of curves represented by y^2 = 4ax is known as:
  • Step 1: Identify the equation given, which is y^2 = 4ax.
  • Step 2: Recognize that this equation is in the standard form of a parabola.
  • Step 3: Understand that 'a' is a constant that affects the width and direction of the parabola.
  • Step 4: Realize that as 'a' changes, the shape of the parabola changes, but it remains a parabola.
  • Step 5: Conclude that the family of curves represented by this equation is indeed a family of parabolas.
  • Parabolas – The equation y^2 = 4ax describes a standard form of a parabola that opens to the right.
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