If focal distance of a point P on the parabola `y^(2)=4ax` whose abscissa is 5 10, then find the value of a.

Explanation

To solve the problem, we need to find the value of \( a \) for the parabola defined by the equation \( y^2 = 4ax \) given that the focal distance of a point \( P \) on the parabola with an abscissa of 5 is 10.

### Step-by-Step Solution:

1. **Understand the Parabola Equation**: The equation of the parabola is given as \( y^2 = 4ax \). Here, \( a \) is a constant that determines the distance from the vertex to the focus.

2. **Identify the Focal Distance**: The focal distance \( s \) for a point \( P \) on the parabola is given by the formula:
\[ s = x + a \]
where \( x \) is the abscissa of the point \( P \).

3. **Substitute Given Values**: We are given that the abscissa \( x = 5 \) and the focal distance \( s = 10 \). Substituting these values into the focal distance formula gives:
\[ 10 = 5 + a \]

4. **Solve for \( a \)**: Rearranging the equation to solve for \( a \):
\[ a = 10 - 5 \]
\[ a = 5 \]

5. **Conclusion**: The value of \( a \) is \( 5 \).

### Final Answer:
The value of \( a \) is \( 5 \).