Math, asked by gayathri843, 6 months ago

find the equation of the circumcircle of the triangle formed by the straight lines given in each of the following 2 X + y =4 ,x + y =6, X + 2 y = 5​

Answers

Answered by yamankashyap2912
0

Answer:

90.5

Step-by-step explanation:

x+y=6...(1)

2x+y=4....(2)

x+2y=5....(3)

solve (1) and (2)

from (1), y=6−x

sub in (2)

2x+6−x=4

x=4−6=−2

y=6−x=6−(−2)=8

(x,y)=(−2,8)

Solve (2) and (3)

from (2) y=4−2x

sub in (3)

x+2(4−2x)=5

x+8−4x=5

−3x−5−8

−3x=−3

x=1

2(1)+y=4

y=+2

(1,+2)

Solve (1) and (3)

x=5−2y

sub in (1)

5−2y+y=6

y=−1

x−1=6

x=6+1

x=7

(7,−1)

Equation of circumscribing

(x−a)

2

+(y−b)

2

=r

2

....(4)

Substitute value of x and y in (4)

(−2,8) in (4) ⇒ a

2

+b

2

+4a−16+68=r

2

....(5)

(1,+2) in (4) ⇒ a

2

+b

2

−2a−4b+5=r

2

....(6)

(7,−1) in (4) ⇒ a

2

+b

2

−14a+2b+50=r

2

.......(7)

solve (5) and (7) we get a−b=−1....(8)

solve (7) and (6) we get 2b−4a=−13...(9)

solve (8) and (9)

we get a=

2

15

,b=

2

17

Substitute a and b in (5) we get r

2

=90.5

equation is

[x−

2

15

]

2

+[y−

2

17

]

2

=90.5

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