The directrix of the parabola `y^(2) = - 8x" is", x = 2 ` .

Answer

To solve the problem, we need to find the directrix of the parabola given by the equation \( y^2 = -8x \).

### Step-by-Step Solution:

1. **Identify the standard form of the parabola**:
The given equation \( y^2 = -8x \) is in the standard form of a parabola that opens to the left, which is \( y^2 = -4ax \).

2. **Compare the given equation with the standard form**:
From the standard form \( y^2 = -4ax \), we can see that \( -4a = -8 \).

3. **Solve for \( a \)**:
To find \( a \), we set up the equation:
\[ -4a = -8 \]
Dividing both sides by -4 gives:
\[ a = 2 \]

4. **Determine the directrix**:
For a parabola of the form \( y^2 = -4ax \), the directrix is given by the equation \( x = -a \). Since we found \( a = 2 \):
\[ x = -2 \]

5. **Conclusion**:
The directrix of the parabola \( y^2 = -8x \) is \( x = -2 \).

### Final Answer:
The directrix of the parabola \( y^2 = -8x \) is \( x = -2 \).

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