What is the axis of symmetry for the parabola given by the equation y^2 = 6x?

Practice Questions

Q1
What is the axis of symmetry for the parabola given by the equation y^2 = 6x?
  1. x-axis
  2. y-axis
  3. y = x
  4. x = 0

Questions & Step-by-Step Solutions

What is the axis of symmetry for the parabola given by the equation y^2 = 6x?
  • Step 1: Identify the given equation of the parabola, which is y^2 = 6x.
  • Step 2: Recognize that this equation is in the form y^2 = 4px, where p is a constant.
  • Step 3: Compare the equation y^2 = 6x with y^2 = 4px to find p. Here, 4p = 6.
  • Step 4: Solve for p by dividing both sides of the equation by 4: p = 6/4 = 1.5.
  • Step 5: Understand that for parabolas in the form y^2 = 4px, the axis of symmetry is the x-axis.
  • Step 6: Conclude that the axis of symmetry for the parabola y^2 = 6x is the x-axis.
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