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Question
Find the centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
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Solution
Comparing the equation
x2 + y2 − 2x + 4y − 4 = 0
with the equation
x2 + y2 + 2gx + 2fy + c = 0, we get,
2g= − 2, 2f = 4 and c = − 4
∴ g = − 1, f = 2 and c = − 4
∴ centre of the circle = (− g, − f) = (1, − 2)
and radius of the circle = `sqrt("g"^2 + f^2 - "c"`
= `sqrt((-1)^2 + (2)^2 - (- 4))`
= `sqrt(1 + 4 + 4)`
= 3.
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