The equation of the directrix of the parabola `x^(2) = 8y` is

Options

A. `y =-2`
B. `x=-2`
C. `y=-8`
D. `x = 8`

Answer

To find the equation of the directrix of the parabola given by the equation \( x^2 = 8y \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The given equation \( x^2 = 8y \) can be compared to the standard form of a parabola that opens upwards, which is given by:
\[ x^2 = 4ay \]
From this comparison, we can identify that \( 4a = 8 \).

### Step 2: Solve for \( a \)
To find the value of \( a \), we solve the equation:
\[ 4a = 8 \]
Dividing both sides by 4, we get:
\[ a = \frac{8}{4} = 2 \]

### Step 3: Determine the equation of the directrix
For a parabola that opens upwards, the equation of the directrix is given by:
\[ y = -a \]
Substituting the value of \( a \) we found:
\[ y = -2 \]

### Step 4: Write the final answer
Thus, the equation of the directrix of the parabola \( x^2 = 8y \) is:
\[ \boxed{y = -2} \]

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