If `e_(1) and e_(2)` be the eccentricities of the two rectangular hyperbolas `xy=c^(2)` and `xy=d^(2)` referred to asymptotes as axes, then
`e_(1)-e_(2)` = …………..

Answer

To solve the problem, we need to find the difference between the eccentricities \( e_1 \) and \( e_2 \) of the two rectangular hyperbolas given by the equations \( xy = c^2 \) and \( xy = d^2 \).

### Step-by-Step Solution:

1. **Understanding Rectangular Hyperbolas**:
- A rectangular hyperbola is defined as a hyperbola where the transverse and conjugate axes are equal, which means \( a = b \). The standard form of a rectangular hyperbola is \( xy = k^2 \).

2. **Eccentricity of a Rectangular Hyperbola**:
- The eccentricity \( e \) of a rectangular hyperbola can be expressed as:
\[ e = \sqrt{1 + \frac{b^2}{a^2}} \]
- Since for a rectangular hyperbola \( a = b \), we can substitute \( b = a \):
\[ e = \sqrt{1 + \frac{a^2}{a^2}} = \sqrt{1 + 1} = \sqrt{2} \]

3. **Calculating Eccentricities**:
- For the hyperbola \( xy = c^2 \):
- Here, we can identify \( a = c \) and \( b = c \) (since it's rectangular).
- Thus, the eccentricity \( e_1 \) is:
\[ e_1 = \sqrt{2} \]
- For the hyperbola \( xy = d^2 \):
- Similarly, we identify \( a = d \) and \( b = d \).
- Thus, the eccentricity \( e_2 \) is:
\[ e_2 = \sqrt{2} \]

4. **Finding the Difference**:
- Now we need to find \( e_1 - e_2 \):
\[ e_1 - e_2 = \sqrt{2} - \sqrt{2} = 0 \]

### Final Answer:
\[ e_1 - e_2 = 0 \]