10. Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line .
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Condition 1: the circle passes through points (4,1) and (6,5)
Now, Condition 2:centre is on the line .
From condition 1 and condition 2
Now lets substitute this value of h and k in condition 1 to find out r
So now, the Final Equation of the circle is
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