The length of the latus rectum of the parabola `x^(2) = -28y` is

Options

A. 28 units
B. 7 units
C. 14 units
D. 21 units

Answer

To find the length of the latus rectum of the parabola given by the equation \( x^2 = -28y \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The standard form of a parabola that opens downwards is given by:
\[ x^2 = -4ay \]
where \( a \) is the distance from the vertex to the focus.

### Step 2: Compare the given equation with the standard form
The given equation is:
\[ x^2 = -28y \]
By comparing this with the standard form \( x^2 = -4ay \), we can identify:
\[ -4a = -28 \]

### Step 3: Solve for \( a \)
To find \( a \), we can set up the equation:
\[ 4a = 28 \]
Dividing both sides by 4 gives:
\[ a = \frac{28}{4} = 7 \]

### Step 4: Calculate the length of the latus rectum
The length of the latus rectum \( L \) of a parabola is given by the formula:
\[ L = 4a \]
Substituting the value of \( a \) we found:
\[ L = 4 \times 7 = 28 \]

### Conclusion
Thus, the length of the latus rectum of the parabola \( x^2 = -28y \) is \( 28 \) units.

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