Question

3x + y = 0.
Find the circumcenter of the triangle whose sides are given by x+y+2=0, 5x-y-2 = 0 and
x-2y + 5 = 0.​

Answer 1

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

)