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
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