# Find the centre and radius of the following: x2 + y2 − 2x + 4y − 4 = 0 - Mathematics and Statistics

Sum

Find the centre and radius of the following:

x2 + y2 − 2x + 4y − 4 = 0

#### 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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