Length of latus -rectum of the hyperbola `(x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 ` is ................. .

Answer

To find the length of the latus rectum of the hyperbola given by the equation \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Standard Form of the Hyperbola**:
The given equation is already in the standard form of a hyperbola, which is \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\).

2. **Recall the Formula for the Length of the Latus Rectum**:
For a hyperbola in the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), the length of the latus rectum (L) is given by the formula:
\[ L = \frac{2b^2}{a} \]

3. **Substitute the Values**:
In this case, we do not have specific values for \(a\) and \(b\), but we can express the length of the latus rectum in terms of \(a\) and \(b\):
\[ L = \frac{2b^2}{a} \]

4. **Final Answer**:
Therefore, the length of the latus rectum of the hyperbola is:
\[ \text{Length of the latus rectum} = \frac{2b^2}{a} \]