Assertion: The plot of volume `(V)` versus pressure `(P)` at constant temperature is a hyperbola in the first quadrant.
Reason: `V prop 1//P` at constant temperature.

Options

A. If both (`A`) and (`R`) are correct and (`R`) is the correct explanation of (`A`).
B. If both (`A`) and (`R`) are correct, but (`R`) is not the correct explanation of (`A`).
C. If (`A`) is correct, but (`R`) is incorrect.
D. If (`A`) is incorrect, but (`R`) is correct.

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the plot of volume (V) versus pressure (P) at constant temperature is a hyperbola in the first quadrant.
- According to Boyle's Law, at constant temperature, the volume of a gas is inversely proportional to its pressure.

2. **Understanding the Reason**:
- The reason states that V is proportional to \( \frac{1}{P} \) at constant temperature.
- This means that if pressure increases, volume decreases, and vice versa, which is a characteristic of an inverse relationship.

3. **Mathematical Representation**:
- From Boyle's Law, we can express this relationship mathematically as:
\[ PV = k \]
where \( k \) is a constant (nRT, where n is the number of moles, R is the gas constant, and T is the temperature).

4. **Graphical Representation**:
- Rearranging the equation gives:
\[ V = \frac{k}{P} \]
- This equation represents a hyperbola when plotted on a graph with volume (V) on the y-axis and pressure (P) on the x-axis.

5. **First Quadrant**:
- The graph will only exist in the first quadrant because both volume (V) and pressure (P) must be positive values for real gases.

6. **Conclusion**:
- Since the reason correctly explains the assertion, both the assertion and reason are true. Therefore, the correct answer to the question is that the assertion is true and the reason is a correct explanation of the assertion.

### Final Answer:
- The assertion is true, and the reason is a correct explanation for the assertion.