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The family of curves given by y^2 = 4ax represents which type of conic section?

Practice Questions

Q1
The family of curves given by y^2 = 4ax represents which type of conic section?
  1. Circle
  2. Ellipse
  3. Parabola
  4. Hyperbola

Questions & Step-by-Step Solutions

The family of curves given by y^2 = 4ax represents which type of conic section?
  • 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: Note that in the equation y^2 = 4px, the variable y is squared and the variable x is not, indicating a vertical orientation.
  • Step 4: Since the equation is y^2 = 4ax, it shows that the parabola opens to the right because 'a' is positive.
  • Step 5: Conclude that the family of curves represented by this equation is a parabola that opens to the right.
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