show that the points (5,5),(6,4),(-2,4) and (7,1) all lie on a circle, and find its equation, centre and radius.
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show that the points (5,5),(6,4),(-2,4) and (7,1) all lie on a circle, and find its equation, centre and radius.
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Answer:
Equation of circle with a center (a,b)
(x-a)^2 +(y-b)^2 = r^2
(5-a)^2 + (5-b)^2 =r^2 --(A)
(6-a)^2 + (4-b)^2 =r^2 --(B)
(-2-a)^2 + (4-b)^2 =r^2 --(C)
(6-a)^2 + (4-b)^2 =r^2 --(B)
(-2-a)^2 + (4-b)^2 =r^2 --(C)
-------------------------------------- -
(36-12a+a^2) -(4+4a+a^2)=0
32-16a =0
a=2
(5-2)^2 + (5-b)^2 =r^2 ---(A)
(6-2)^2 + (4-b)^2 =r^2 ---(B)
--------------------------------------------- -
-7 +(25-10b+b^2)-(16-8b+b^2) =0
-7+9-2b=0
b=1
(6-2)^2 + (4-1)^2 =r^2 ---(B)
16+9=r^2
r=5
equation
(x-2)^2 +(y-1)^2 = 25
(7,1) lies on a cirle too
Step-by-step explanation:
Equation of circle with a center (a,b)
(x-a)^2 +(y-b)^2 = r^2
Answer:
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Step-by-step explanation: