Statement I The line `y=mx+a/m` is tangent to the parabola `y^2=4ax` for all values of m.
Statement II A straight line y=mx+c intersects the parabola `y^2=4ax` one point is a tangent line.

Answer

To solve the problem, we need to analyze both statements regarding the parabola \( y^2 = 4ax \) and the line equations provided.

### Step 1: Analyze Statement II
We start with the line equation given in Statement II:
\[ y = mx + c \]
We need to find the points of intersection with the parabola:
\[ y^2 = 4ax \]
Substituting \( y = mx + c \) into the parabola equation:
\[ (mx + c)^2 = 4ax \]
Expanding the left side:
\[ m^2x^2 + 2mcx + c^2 = 4ax \]
Rearranging gives us a quadratic equation in \( x \):
\[ m^2x^2 + (2mc - 4a)x + c^2 = 0 \]

### Step 2: Condition for Tangency
For the line to be tangent to the parabola, the quadratic must have exactly one solution, which means the discriminant must be zero:
\[ D = b^2 - 4ac = 0 \]
Here, \( a = m^2 \), \( b = 2mc - 4a \), and \( c = c^2 \). Thus:
\[ (2mc - 4a)^2 - 4(m^2)(c^2) = 0 \]
Expanding this:
\[ 4m^2c^2 - 16amc + 16a^2 - 4m^2c^2 = 0 \]
This simplifies to:
\[ -16amc + 16a^2 = 0 \]
Factoring out \( 16a \):
\[ 16a(a - mc) = 0 \]
Since \( a \neq 0 \), we have:
\[ a = mc \]
Thus, we can express \( c \) in terms of \( a \) and \( m \):
\[ c = \frac{a}{m} \]

### Step 3: Substitute \( c \) Back into the Line Equation
Substituting \( c \) back into the line equation gives:
\[ y = mx + \frac{a}{m} \]
This shows that the line is indeed tangent to the parabola at one point.

### Step 4: Analyze Statement I
Now we analyze Statement I, which states that the line:
\[ y = mx + \frac{a}{m} \]
is tangent to the parabola \( y^2 = 4ax \) for all values of \( m \).

From our previous analysis, we see that for any value of \( m \), the line \( y = mx + \frac{a}{m} \) intersects the parabola at exactly one point, confirming that it is a tangent line.

### Conclusion
Both statements are true:
- Statement I is true because the line is tangent for all values of \( m \).
- Statement II is true as it provides the condition for tangency.

Thus, the final answer is:
- Statement I: True
- Statement II: True