find the equation of the circum_circle of the triangle formed by the straight linnes given in each of the following. 2x+y=4, x+y=6, x+2y=5
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Answer:
Explanation:
Solving given three line the vertices of the triangle are A(1,2),B(−2,8) and C(7,−1)
And let P(a,b) the center of the circle.
Therefore,
PA
2
=PB
2
=PC
2
⇒(a−1)
2
+(b−2)
2
=(a+2)
2
+(b−8)
2
=(a−7)
2
+(b+1)
2
Solving above equations we get a=
2
17
and b=
2
19
Now radius of the circle is PA=
(a−1)
2
+(b−2)
2
=
4
15
2
+
4
15
2
Hence equation of required circle is,
(x−
2
17
)
2
+(y−
2
19
)
2
=PA
2
=
4
15
2
+
4
15
2
⇒x
2
+y
2
−17x−19y+50=0
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