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Question
Find the equation of the circle through the points (1, 0), (– 1, 0) and (0, 1)
Solution
Let the general equation of the circle be
x2 + y2 + 2gx + 2fy + c = 0
It passes through the points (1, 0), (– 1, 0) and (0, 1)
1 + 0 + 2g + c = 0
2g + c = – 1 .......(1)
1 + 0 – 2g + c = 0
– 2g + c = – 1 .......(2)
0 + 1 + 0 + 2f + c = 0
2f + c = – 1
(1) + (2)
⇒ 2c = – 2
c = – 1
Substitute in equation (1)
2g – 1 = – 1
2g = 0
g = 0
Substitute in equation (3)
2f – 1 = – 1
2f = – 1 + 1
2f = 0
f = 0
Therefore, the required equation of the circle
x2 + y2 – 1 = 0
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