find the circumcentre of the triangle whose vertices are given by x+y+2=0, 5x-y-2=0 and x-2y +5=0
Answers
Answer:
- x+y+2=0,
- 5x-y-2=0
- x-2y +5=0
3x−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:
Answer:
-1/3,2/3
Explanation:
we can do sa=sb=sc