If the center of a circle is (2a, a – 7) then find the values of a, if the circle passes through the point (11, - 9) and has diameter 
units.
Using the given condition;
As distance between two points (x1, y1) and (x2, y2);
d = 
So,
Distance between the centre C (2a, a – 7) and the point P (11, - 9), which lie on the circle = Radius of circle.
…….(i)
Given that,
Length of diameter = 
By putting this value in Eq. (i),
We get;
By squaring both sides,
We get;
50 = (11 – 2a)2 + (2 + a)2
→ 50 = 121 + 4a2 – 44a + 4 + a2 + 4a
→ 5a2 – 40a + 75 = 0
→ a2 – 8a + 15 = 0
→ a2 – 5a – 3a + 15 = 0
By factorization method;
a(a – 5) – 3(a – 5) = 0
(a – 5)(a – 3) = 0
a = 3, 5
Hence, the values of a are 5 and 3.
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