Find the circumcentre of the triangle whose sides are given by x+y=0, 2x+y+5=0 and x - y = 0.
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Answer:
A
3x−y−5=0
⇒y=3x−5
B
x+2y−4=0
y=
2
−1
x+2
C
5x+3y+1=0
y=
3
−5
x−
3
1
D
3x−5=
2
−1
x+2
⇒D(2,1)
E
3x−5=
3
−5
x−
3
1
⇒E(1,−2)
F
2
−1
x+2=
3
−5
x−
3
1
⇒F(−2,3)
Use these point to make a circle.
D=(2−h)
2
+(1−k)
2
=r
2
E=(1−h)
2
+(−2−k)
2
=r
2
F=(−2−h)
2
+(3−k)
2
=r
2
⇒h=
7
−6
,k=
7
2
,r=
7
5
17
Circumcenter=(
7
−6
,
7
2
)
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