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

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

Options:

Correct Answer: y-axis

Solution:

The axis of symmetry for the parabola y^2 = 4px is the x-axis.

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

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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