Equation of the circle passing through the points (1, 2), (2, -1) and (3, 5) is
(1) 9(x2 + y2) – 87x – 29y + 100 = 0
(2) 10(x2 + y2) - 87x - 29y + 100 = 0
(3) 3(x2 + y2) – 87x – 29y + 10 = 0
(4) 5(x2 + y2) – 12x - 29y + 5 = 0
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Given: circle Passing through points (1, 2), (2, -1) and (3, 5)
To find: Equation of circle
Solution: for a given circle (x-x1) ^2+ (y-y1) ^2= r^2
in which (x1, y1) are points and r is radius of circle
All points of a circle that are on the circle are on the same distance from the center of the circle.
since it is given that the points (1, 2), (2, -1) and (3, 5) are on the circle.
therefore we can form these equation:
(x−1)2+(y−1)2=(x−2)2+(y+1)2
(x−2)2+(y+1)2=(x−3)2+(y−2)2
solving these equation, we will get the reduced equation as
2x−4y=32
x+6y=8
and further solving these two equation, we will get values of x, y
(x,y)=(5/2,1/2)
on putting this value in one of the equation we will get the radius of the circle
R^2= 5/2
therefore radius of the circle will be √(5/2)
Hence we will get the equation of circle as
Hence we will get the equation of circle as (x−5/2)^2+(y−1/2)^2=5/2