Find the length of latusrectum intersect at the focus S its coordinate are detained by solving.

Answer

To find the length of the latus rectum of a parabola that intersects at the focus, we can follow these steps:

### Step 1: Understand the Parabola and its Properties
A parabola is defined as the set of all points equidistant from a point called the focus and a line called the directrix. The length of the latus rectum is a line segment perpendicular to the axis of symmetry of the parabola that passes through the focus.

### Step 2: Identify the Formula
The length of the latus rectum (L) of a parabola can be calculated using the formula:
\[ L = 4p \]
where \( p \) is the distance from the vertex to the focus.

### Step 3: Determine the Value of \( p \)
To find \( p \), we need to know the specific equation of the parabola or its geometric properties. For example, if the parabola opens upwards and is given in standard form as:
\[ y^2 = 4px \]
then \( p \) is the coefficient of \( x \) divided by 4.

### Step 4: Substitute \( p \) into the Formula
Once we have found \( p \), we can substitute it into the formula for the length of the latus rectum:
\[ L = 4p \]

### Step 5: Calculate the Length of the Latus Rectum
Perform the calculation to find the length of the latus rectum.

### Example Calculation
Assuming we have a parabola defined by \( y^2 = 16x \):
1. Here, \( 4p = 16 \) implies \( p = 4 \).
2. Now, substituting into the formula:
\[ L = 4p = 4 \times 4 = 16 \]

Thus, the length of the latus rectum is 16.

### Final Answer
The length of the latus rectum is 16.

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