Let a line `y = mx ( m gt 0)` intersect the parabola, `y^2 = 4x` at a point P, other than the origin. Let the tangent to it at P meet the x-axis at the point Q. If area `(Delta OPQ)=8` sq. units, then m is equal to _______ .

Explanation

To solve the problem, we need to find the value of \( m \) such that the area of triangle \( OPQ \) is 8 square units, where \( O \) is the origin, \( P \) is a point on the parabola \( y^2 = 4x \), and \( Q \) is the point where the tangent at \( P \) meets the x-axis.

### Step-by-Step Solution:

1. **Identify the point \( P \) on the parabola**:
The parabola is given by the equation \( y^2 = 4x \). A point \( P \) on this parabola can be represented as \( P(t) = (t^2, 2t) \), where \( t \) is a parameter.

2. **Equation of the tangent at point \( P \)**:
The equation of the tangent to the parabola at point \( P(t) \) is given by:
\[ 2ty = x + t^2 \]
Rearranging this gives:
\[ x = 2ty - t^2 \]

3. **Find the point \( Q \) where the tangent meets the x-axis**:
The x-axis is defined by \( y = 0 \). Substituting \( y = 0 \) into the tangent equation:
\[ x = 2t(0) - t^2 = -t^2 \]
Thus, the coordinates of point \( Q \) are \( Q(-t^2, 0) \).

4. **Coordinates of points \( O \), \( P \), and \( Q \)**:
- \( O(0, 0) \)
- \( P(t) = (t^2, 2t) \)
- \( Q(-t^2, 0) \)

5. **Area of triangle \( OPQ \)**:
The area \( A \) of triangle \( OPQ \) can be calculated using the formula:
\[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Substituting the coordinates:
\[ A = \frac{1}{2} \left| 0(2t - 0) + t^2(0 - 0) + (-t^2)(0 - 2t) \right| \]
Simplifying this gives:
\[ A = \frac{1}{2} \left| -t^2(-2t) \right| = \frac{1}{2} \left| 2t^3 \right| = t^3 \]
We know from the problem statement that the area \( A = 8 \):
\[ t^3 = 8 \implies t = 2 \]

6. **Relate \( t \) to \( m \)**:
From the line equation \( y = mx \), we also know that:
\[ 2t = m(t^2) \]
Substituting \( t = 2 \):
\[ 2(2) = m(2^2) \implies 4 = 4m \implies m = 1 \]

### Final Answer:
Thus, the value of \( m \) is:
\[ \boxed{1} \]