Statement -1 : The lines `y = pm b/a xx ` are known as the asymptotes of the hyperbola `x^(2)/a^(2) - y^(2)/b^(2) - 1 = 0 `.
because
Statement -2 : Asymptotes touch the curye at any real point .

Options

A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True, Statement - 2 is NOT a correct explanation for Statement - 1
C. Statement - 1 is True , Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True

Answer

To solve the problem, we need to analyze the two statements provided regarding the hyperbola and its asymptotes.

### Step-by-Step Solution:

1. **Understanding the Hyperbola Equation**:
The given hyperbola is represented by the equation:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
This is the standard form of a hyperbola that opens horizontally.

**Hint**: Identify the standard form of the hyperbola and recognize its components (a and b).

2. **Finding the Asymptotes**:
The asymptotes of a hyperbola can be derived from the equation by setting the right-hand side to zero:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 0 \]
Rearranging this gives:
\[ \frac{y^2}{b^2} = \frac{x^2}{a^2} \]
From this, we can express \(y\) in terms of \(x\):
\[ y^2 = \frac{b^2}{a^2} x^2 \]
Taking the square root, we find:
\[ y = \pm \frac{b}{a} x \]
Thus, the equations of the asymptotes are:
\[ y = \pm \frac{b}{a} x \]

**Hint**: Set the hyperbola equation to zero to derive the asymptote equations.

3. **Analyzing Statement 1**:
Statement 1 claims that the lines \(y = \pm \frac{b}{a} x\) are the asymptotes of the hyperbola. From our derivation, we have confirmed that this statement is true.

**Hint**: Verify the derived asymptote equations against Statement 1.

4. **Analyzing Statement 2**:
Statement 2 claims that the asymptotes touch the hyperbola at any real point. However, asymptotes do not intersect the hyperbola at any finite point; they only approach the hyperbola as they extend towards infinity. Therefore, this statement is false.

**Hint**: Understand the definition of asymptotes and their behavior relative to the hyperbola.

5. **Conclusion**:
- Statement 1 is **True**.
- Statement 2 is **False**.

### Final Answer:
- Statement 1: True
- Statement 2: False