Question

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Answer 1

Step-by-step explanation:

I hope u agree with the answer .

Answer 2

.

Step-by-step explanation:

Let A(−2,−3), B(−1,0) and C(7,−6) be the vertices of the triangle. P(x,y) be the required circumcentre.

Also, PA  2  =PB  

2  =PC  

2  =Radius

Distance between two points =  

(x  2  −x  1  )  

2  +(y  2  −y  1  )  2

 So,

PA=  (x−(−2))  

2

+(y−(−1))  

2

PA  

2

=(x+2)  

2  +(y+1)  

2

PA  

2  =x  

2  +4+4x+y  

2  +9+6y..........(1)

PB=  (x−(−1))  

2

+(y−(0))  

2

PB  

2  =(x+1)  

2

+y  

2

PB  

2  =x  2  +1+2x+y  2  ...........(2)

PC=  (x−7)  2  +(y−(−6))  2

PC  

2  =(x−7)  2  +(y+6)  

2

PC  

2  =x  

2  +49−14x+y  

2  +36+12y...........(3)

from (1) and (2) we get,

⇒x  

2  +4+4x+y  

2  +9+6y=x  

2

+1+2x+y  2

 

⇒4x+6y+13=1+2x

⇒2x+6y+12=0

⇒x+3y+6=0

from (1) and (3) we get,

x  2  +1+2x+y  2  =x  

2  +49−14x+y  

2

+36+12y

⇒1+2x=49−14x+36+12y

⇒2x−12y+14x=84

⇒16x−12y=84

⇒4x−3y=21

4(−3y−6)−3y=21

⇒−12y−24−3y=21

⇒15y=−45

y=  15

−45  =−3

x=−6+9=3

∴vertices of circumcentre=(3,−3)

hope its helpful....

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