Find the directrix of the parabola y^2 = -8x.

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Question: Find the directrix of the parabola y^2 = -8x.

Options:

Correct Answer: x = -2

Solution:

For the parabola y^2 = 4px, here 4p = -8, so p = -2. The directrix is given by x = -p, which is x = 2.

Find the directrix of the parabola y^2 = -8x.

Find the directrix of the parabola y^2 = -8x.

Step 1: Identify the standard form of the parabola equation, which is y^2 = 4px.
Step 2: Compare the given equation y^2 = -8x with the standard form to find the value of 4p.
Step 3: In the equation y^2 = -8x, we see that 4p = -8.
Step 4: To find p, divide -8 by 4: p = -8 / 4 = -2.
Step 5: The directrix of a parabola is given by the formula x = -p.
Step 6: Substitute the value of p into the directrix formula: x = -(-2) = 2.
Step 7: Therefore, the directrix of the parabola y^2 = -8x is x = 2.

Parabola Standard Form – Understanding the standard form of a parabola and how to identify parameters such as p.
Directrix of a Parabola – Knowing how to find the directrix from the value of p in the equation of a parabola.