A rectangle `A B C D` is inscribed in a circle with a diameter lying along the line `3y=x+10.` If `A` and `B` are the points `(-6,7)a n d(4,7)` respectively, find the area of the rectangle and equation of the circle.

Explanation

To solve the problem step by step, we will first find the equation of the circle and then calculate the area of the rectangle inscribed in it.

### Step 1: Find the center of the circle
Given that the diameter lies along the line \(3y = x + 10\), we can rewrite it in slope-intercept form:
\[ y = \frac{1}{3}x + \frac{10}{3} \]
The center of the circle, denoted as \((h, k)\), lies on this line.
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