What is the directrix of the parabola given by the equation y^2 = 8x?

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Question: What is the directrix of the parabola given by the equation y^2 = 8x?

Options:

Correct Answer: x = -2

Solution:

The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.

What is the directrix of the parabola given by the equation y^2 = 8x?

What is the directrix of the parabola given by the equation y^2 = 8x?

Step 1: Identify the given equation of the parabola, which is y^2 = 8x.
Step 2: Rewrite the equation in the standard form of a parabola, which is (y - k)^2 = 4p(x - h).
Step 3: Compare y^2 = 8x with the standard form. Here, we can see that 4p = 8.
Step 4: Solve for p by dividing 8 by 4. So, p = 8 / 4 = 2.
Step 5: The vertex of the parabola is at the origin (0, 0), which means h = 0 and k = 0.
Step 6: The directrix of a parabola is given by the formula x = h - p.
Step 7: Substitute h = 0 and p = 2 into the formula: x = 0 - 2.
Step 8: Simplify the equation to find the directrix: x = -2.

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