Find the circumcentre of the triangle whose vertices are given by x+y+

1.	Find the circumcentre of the triangle whose vertices are given by x+y+2=0, 5x-y-2=0 and x-2y +5=0
Answer» x+y+2=0,5x-y-2=0x-2y +5=03x−y−5=0....(i) x+2y−4=0.....(ii) 5x+3y+1=0.....(iii) First find the vertices of the △ Solving (i) and (ii) simultaneously x 1 =2,y 1 =1 ∴A(2,1) SIMILARLY solving (ii) and (iii) simultaneously x 2 =−2,y 2 =3 ∴ B(−2,3) Finally from (i) and (iii) x 3 =1,y 3 =−2 C(1,−2) Let the equation of CIRCLE through A,B,C be x 2 +y 2 +2gx+2fy+c=0 put the coordinates of A(2,1) 4+1+4g+2g+c=0 4g+2f+c=−5....(iv) Similarly by putting coordinates of B(−2,3) in the circle equation we get 4g−6g−c=13....(v) and putting C(1,−2) 2g−4f+c=−5....(vi) Solving (iv), (v), (vi) simultaneously f=− 7 2 ,G= 7 6 ,c=− 7 5.5 The circumcentre of the circle ≡(−g,−f) ≡(− 7 6 , 7 2 )Explanation:

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