Find the centre and radius of the circles.
$x^{2} + y^{2} - 4 x - 8 y - 5 = 0$

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Solution

Given the equation of the circle is $x^{2} + y^{2} - 4 x - 8 y - 5 = 0$ which can be written as,
$x^{2} - 4 x + 4 + y^{2} - 8 y + 16 = 25$
or, $(x - 2)^{2} + (y - 4)^{2} = 5^{2}$ .
From this equation it is clear that the cente is at $(2, 4)$ and radius is $5$ units.

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