6. Exemplar - Find the value of 'a'

The centre of a circle is \((2a, a – 7)\). Find the values of \(a\) if the circle passes through the point \((11, –9)\) and has diameter \(10\sqrt 2\) units.

 

 

The value of \(a\) is and .

 

[Note: Enter the answer in the ascending order]