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Question
If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.
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Solution
The general equation of the circle is x2 + y2 + 2gx + 2fy + c = 0
Now, it is passing through (0, 0)
∴ c = 0
Also, it is passing through (a, 0)
∴ a2 + 2ag = 0
⇒ a(a + 2g) = 0
⇒a + 2g = 0
Again, it is passing through (0, b)
∴ b2 + 2bf = 0
⇒ b(b + 2f) = 0
⇒b + 2f = 0
The coordinates of its centre are given by
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