Find the equation of the circle circumscribing the rectangle whose sides are `x-3y=4,\ 3x+y=32 ,\ x-3y=14\ a n d\ 3x+y=62.`

Explanation

To find the equation of the circle circumscribing the rectangle defined by the lines \( x - 3y = 4 \), \( 3x + y = 32 \), \( x - 3y = 14 \), and \( 3x + y = 62 \), we will follow these steps:

### Step 1: Find the Intersection Points
We need to find the vertices of the rectangle by solving the equations pairwise.

1. **Intersection of \( x - 3y = 4 \) and \( 3x + y = 32 \)**:
- From \( x - 3y = 4 \), we can express \( x \) in terms of \( y \):
\[
...