Assertion`:-` The trajectory of projectile in `XY` plane is quadratic in `x` and linear in `y` if x is independent of `X-`coordinate.
Reason `:-` `y-`coordinate of trajetory is independent of `x-`coordinate.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the trajectory of a projectile in the XY plane is quadratic in x and linear in y if x is independent of the x-coordinate.

- The trajectory of a projectile is generally described by the equations:
\[ x = u_x t \]
\[ y = u_y t - \frac{1}{2} g t^2 \]
where \( u_x \) and \( u_y \) are the horizontal and vertical components of the initial velocity, and \( g \) is the acceleration due to gravity.

2. **Finding the Relationship**:
- From the equation for \( x \), we can express time \( t \) as:
\[ t = \frac{x}{u_x} \]
- Substituting this expression for \( t \) into the equation for \( y \):
\[ y = u_y \left(\frac{x}{u_x}\right) - \frac{1}{2} g \left(\frac{x}{u_x}\right)^2 \]
- Simplifying this gives:
\[ y = \frac{u_y}{u_x} x - \frac{g}{2 u_x^2} x^2 \]
- This shows that \( y \) is a quadratic function of \( x \) (since it includes an \( x^2 \) term) and thus confirms that the trajectory is quadratic in \( x \).

3. **Understanding the Reason**:
- The reason states that the y-coordinate of the trajectory is independent of the x-coordinate.
- However, from our earlier derivation, we see that \( y \) is actually dependent on \( x \) because \( y \) is expressed as a function of \( x \).

4. **Conclusion**:
- The assertion is true because the trajectory is indeed quadratic in \( x \).
- The reason is false because the y-coordinate is dependent on the x-coordinate.

### Final Answer:
- **Assertion**: True
- **Reason**: False
- Therefore, the correct option is that the assertion is true and the reason is false.