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Question
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
Solution
Comparing the equation x2 + y2 − x +2y − 3 = 0
with x2 + y2 + 2gx + 2fy + c = 0, we get,
2g = − 1, 2f = 2 and c = − 3
∴ g = `-1/2`, f = 1 and c = − 3
∴ centre of the circle = `(-"g", -"f") = (1/2, -1)`
and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`
= `sqrt((-1/2)^2 + (1)^2 - (-3))`
= `sqrt(1/4 + 1 + 3)`
= `sqrt(17)/2`.
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