Let A (2,3), B (3,-1) and C (-3,2) be three points. If the centre of the circle passing through A, B and C is (h, k) , then 2 k-4 h=

Step-by-step solution

Let ( h , k ) be the centre of the circle Now A O=C O A O^2=C O^2 aligned & (2-h)^2+(3-k)^2 & =(3+h)^2+(2-k)^2 & k=-5 h...(i) aligned aligned & and AO = BO A O^2=B O^2 & (2-h)^2+(3-k)^2=(3-h)^2+(1+k)^2 & 2 h-8 k=-3...(ii) aligned after solving (i) & (ii), we get aligned & h= -1 14 , k= 5 14 & so, 2 k-4 h= 10 14 + 4 14 =1 aligned