The directrix of the parabola `y^(2) = 12x, "is " x - 3 ` .

Answer

To solve the problem, we need to analyze the given parabola equation and its properties, particularly focusing on the directrix.

### Step-by-Step Solution:

1. **Identify the standard form of the parabola**:
The given equation of the parabola is \( y^2 = 12x \). This can be compared with the standard form of a parabola that opens to the right, which is \( y^2 = 4ax \).

2. **Determine the value of \( a \)**:
From the standard form \( y^2 = 4ax \), we can see that \( 4a = 12 \). To find \( a \), we divide both sides by 4:
\[ a = \frac{12}{4} = 3 \]

3. **Identify the directrix**:
The directrix of a parabola in the form \( y^2 = 4ax \) is given by the equation \( x = -a \). Substituting the value of \( a \) we found:
\[ x = -3 \]

4. **Compare with the given directrix**:
The problem states that the directrix is \( x - 3 \). We can rewrite this as:
\[ x = 3 \]
However, we found that the directrix is \( x = -3 \).

5. **Conclusion**:
The directrix of the parabola \( y^2 = 12x \) is indeed \( x = -3 \), which confirms that the given directrix \( x - 3 \) is incorrect.

### Final Answer:
The directrix of the parabola \( y^2 = 12x \) is \( x = -3 \).

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