Q) The centre of a circle is (2a, a-7). Find the values of ‘a’ if the circle passes through the point (11,-9). Radius of the circle is 5√2cm.

Ans: 

Let’s find out radius of the circle by co-ordinate method.
Therefore, (2a – 11)² + (a -7 + 9)² = (5√2 )²

or (4a² + 121 – 44a) + ((a-7)² + 81 + 18(a-7) = 50

or (4a² +121 – 44a) + (a² + 49 – 14a) + 81+18a – 126) = 50

or 5a² – 40 a + 75 = 0

or (a – 5) (5a – 15) = 0

a = 5 and a = 3

Therefore, The circle passes through the given point for 2 values i.e. a = 5 and a =3.