If the length of the transverse and conjuigate axes of hyperbola be 8 and 6 respectively, then the difference of focal distance of any point of the hyperbola will be

Options

A. 8
B. 6
C. 14
D. 2

Answer

To solve the problem, we need to find the difference of the focal distances of any point on the hyperbola given the lengths of the transverse and conjugate axes.

### Step-by-Step Solution:

1. **Identify the lengths of the axes**:
- The length of the transverse axis (2A) is given as 8.
- The length of the conjugate axis (2B) is given as 6.

2. **Calculate A and B**:
- Since the length of the transverse axis is 2A, we have:
\[ 2A = 8 \implies A = \frac{8}{2} = 4 \]
- Since the length of the conjugate axis is 2B, we have:
\[ 2B = 6 \implies B = \frac{6}{2} = 3 \]

3. **Use the focal property of the hyperbola**:
- The focal property states that for any point P on the hyperbola, the difference of the distances to the two foci (S and S') is equal to the length of the transverse axis (2A).
- Therefore, we can write:
\[ |PS - PS'| = 2A \]

4. **Substitute the value of A**:
- We already calculated A as 4, so:
\[ |PS - PS'| = 2 \times 4 = 8 \]

5. **Conclusion**:
- The difference of the focal distances of any point on the hyperbola is 8.

### Final Answer:
The difference of focal distance of any point of the hyperbola is **8**.