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What is the general form of the family of curves represented by y^2 = 4ax?

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Question: What is the general form of the family of curves represented by y^2 = 4ax?

Options:

  1. Parabolas opening to the right
  2. Circles with varying centers
  3. Ellipses with varying foci
  4. Hyperbolas with varying asymptotes

Correct Answer: Parabolas opening to the right

Solution: 

The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of \'a\'.

What is the general form of the family of curves represented by y^2 = 4ax?

Practice Questions

Q1
What is the general form of the family of curves represented by y^2 = 4ax?
  1. Parabolas opening to the right
  2. Circles with varying centers
  3. Ellipses with varying foci
  4. Hyperbolas with varying asymptotes

Questions & Step-by-Step Solutions

What is the general form of the family of curves represented by y^2 = 4ax?
Correct Answer: y^2 = 4ax
  • Step 1: Identify the equation given, which is y^2 = 4ax.
  • Step 2: Recognize that this equation is a standard form of a parabola.
  • Step 3: Understand that in this equation, 'a' is a constant that affects the shape and position of the parabola.
  • Step 4: Note that the parabola opens to the right because the 'y^2' term is positive and 'x' is on the right side of the equation.
  • Step 5: Realize that different values of 'a' will create different parabolas, all of which open to the right.
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