If AB is a focal chord of the parabola `y^(2)=4ax`, then minimum possible value of `l(AB)` is [l(AB) stands for length of AB] `(a=7//4)`

Answer

To find the minimum possible value of the length of the focal chord \( AB \) of the parabola given by the equation \( y^2 = 4ax \), we can follow these steps:

### Step 1: Understand the properties of the parabola
The parabola \( y^2 = 4ax \) has its focus at the point \( (a, 0) \) and the length of the latus rectum is \( 4a \).

### Step 2: Identify the length of the latus rectum
The length of the latus rectum for the parabola \( y^2 = 4ax \) is given by the formula:
\[ \text{Length of latus rectum} = 4a \]

### Step 3: Substitute the given value of \( a \)
In this case, we are given \( a = \frac{7}{4} \). Therefore, we can calculate the length of the latus rectum:
\[ \text{Length of latus rectum} = 4 \times \frac{7}{4} = 7 \]

### Step 4: Relate the length of the focal chord to the latus rectum
It is known that the minimum length of any focal chord of a parabola is equal to the length of the latus rectum. Thus, we can conclude that:
\[ l(AB) \geq \text{Length of latus rectum} \]

### Step 5: Conclude the minimum value of \( l(AB) \)
Since we have calculated the length of the latus rectum to be \( 7 \), we can say that the minimum possible value of the length of the focal chord \( AB \) is:
\[ l(AB) = 7 \]

### Final Answer
The minimum possible value of \( l(AB) \) is \( \boxed{7} \).

---