The length of the latus rectum of the parabola `y^2=8x` is

Options

A. 4
B. 6
C. 8
D. 10

Answer

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

### Step 1: Identify the standard form of the parabola
The standard form of a parabola that opens to the right is given by:
\[ y^2 = 4ax \]
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:
\[ y^2 = 8x \]
We can see that this matches the standard form \( y^2 = 4ax \) with \( 4a = 8 \).

### Step 3: Solve for \( a \)
To find \( a \), we can set up the equation:
\[ 4a = 8 \]
Dividing both sides by 4 gives:
\[ a = \frac{8}{4} = 2 \]

### 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 \( a \):
\[ L = 4 \times 2 = 8 \]

### Conclusion
Thus, the length of the latus rectum of the parabola \( y^2 = 8x \) is \( 8 \).

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