Q. 73.6( 8 Votes )

Find the equation

Answer :

The general equation of a circle: (x - h)2 + (y - k)2 = r2


…(i), where (h, k) is the centre and r is the radius.


Putting A( - 2, 3), B(5, 2) and c(6, - 1) in (i) we get


h2 + k2 + 4h - 6k + 13 = r2 …(ii)


h2 + k2 - 10h - 4k + 29 = r2 …(iii)and


h2 + k2 - 12h + 2k + 37 = r2 …(iv)


subtracting (ii) from (iii) and also from (iv),


- 14h + 2k + 16 = 0 - 7h + k + 8 = 0


- 16h + 8k + 24 = 0 - 2h + k + 3 = 0


Subtracting,


5h - 5 = 0h = 1


k = - 1


Centre = (1, - 1)


Putting these values in (ii) we get, radius = = 5


Equation of the circle is


(x - 1)2 + {y - ( - 1)}2 = 52


(x - 1)2 + (y + 1)2 = 25.



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