STATEMENT-1 : In simple harmonic motionn graph between celocity `(v)` and displacement `(x)` from mean position is elliptical.
STATEMENT-2 : Relation between `v` and `x` is given by `(v^(2))/(omega^(2)A^(2))+(X^(2))/(A^(2))=1`.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the problem, we need to analyze both statements provided in the question and verify their correctness.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- In SHM, the motion of a particle can be described by its displacement (x) from the mean position and its velocity (v). The velocity changes as the particle moves through its path.

2. **Velocity-Displacement Relationship**:
- The velocity (v) of a particle in SHM can be expressed using the formula:
\[ v = \omega \sqrt{A^2 - x^2} \]
where:
- \( \omega \) is the angular frequency,
- \( A \) is the amplitude,
- \( x \) is the displacement from the mean position.

3. **Rearranging the Velocity Equation**:
- We can rearrange the formula to express \( v^2 \):
\[ v^2 = \omega^2 (A^2 - x^2) \]
- This can be rewritten as:
\[ \frac{v^2}{\omega^2} = A^2 - x^2 \]

4. **Dividing by \( A^2 \)**:
- Now, divide the entire equation by \( A^2 \):
\[ \frac{v^2}{\omega^2 A^2} + \frac{x^2}{A^2} = 1 \]

5. **Identifying the Equation**:
- The resulting equation:
\[ \frac{v^2}{\omega^2 A^2} + \frac{x^2}{A^2} = 1 \]
- This is the standard form of the equation of an ellipse.

6. **Conclusion**:
- Since the relationship between \( v \) and \( x \) is indeed elliptical, we can conclude that:
- **Statement 1** (Assertion) is correct: The graph between velocity and displacement in SHM is elliptical.
- **Statement 2** (Reason) is also correct: The relationship provided is the equation of an ellipse.

7. **Final Answer**:
- Both statements are correct, and Statement 2 provides the correct explanation for Statement 1.