Q. 144.3( 18 Votes )

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Answer :

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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