Let `C_1` and `C_2` be respectively, the parabolas `x^2=y-1` and `y^2=x-1` Let P be any point on `C_1` and Q be any point on `C_2` . Let `P_1` and `Q_1` be the refelections of P and Q, respectively with respect to the line y=x.
If the point `p(pi,pi^2+1)` and `Q(mu^2+1,mu)` then `P_1` and `Q_1` are

Options

A. `(pi^2+1,pi)` and `(mu^2+1,mu)`
B. `(mu^2+1,mu)` and `(mu,mu^2+1)`
C. `(mu,mu^2+1)` =and `(mu,mu^2+1)`
D. `(pi,pi^2+1)` =and `(mu^2,1+mu)`

Answer

To solve the problem, we need to find the reflections of the points \( P \) and \( Q \) on the parabolas \( C_1 \) and \( C_2 \) respectively, with respect to the line \( y = x \).

### Step-by-step Solution:

1. **Identify the Points on the Parabolas:**
- The parabola \( C_1 \) is given by the equation \( x^2 = y - 1 \).
- For the point \( P \), we are given \( P(\pi, \pi^2 + 1) \).
- The parabola \( C_2 \) is given by the equation \( y^2 = x - 1 \).
- For the point \( Q \), we are given \( Q(\mu^2 + 1, \mu) \).

2. **Find the Reflection of Point \( P \):**
- The reflection of a point \( (x, y) \) with respect to the line \( y = x \) is \( (y, x) \).
- Therefore, the reflection of point \( P(\pi, \pi^2 + 1) \) will be:
\[ P_1 = (y, x) = (\pi^2 + 1, \pi) \]

3. **Find the Reflection of Point \( Q \):**
- Similarly, for point \( Q(\mu^2 + 1, \mu) \), the reflection will be:
\[ Q_1 = (y, x) = (\mu, \mu^2 + 1) \]

4. **Final Reflected Points:**
- The reflected point \( P_1 \) is:
\[ P_1 = (\pi^2 + 1, \pi) \]
- The reflected point \( Q_1 \) is:
\[ Q_1 = (\mu, \mu^2 + 1) \]

### Summary of Reflected Points:
- \( P_1 = (\pi^2 + 1, \pi) \)
- \( Q_1 = (\mu, \mu^2 + 1) \)