If the centre of a circle is (2a,a-7) ,then Find the value of a , if the circle passes through the point (11,-9) and has diameter `10sqrt(2)` units .

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We know that the center of the circle is at the point \( (2a, a - 7) \), the circle passes through the point \( (11, -9) \), and the diameter of the circle is \( 10\sqrt{2} \) units.

### Step 2: Calculate the radius
The radius \( r \) of the circle can be found from the diameter:
\[
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