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The equation of the unit circle concentric with $x^{2} + y^{2} - 8 x + 4 y - 8 = 0$ is

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$x^{2} + y^{2} - 8 x + 4 y - 28 = 0$

$x^{2} - y^{2} - 8 x + 4 y - 19 = 0$

$x^{2} + y^{2} - 8 x + 4 y + 19 = 0$

answer is D.

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Detailed Solution

$x^{2} + y^{2} - 8 x + 4 y - 8 = 0$

Centre $(4, - 2), r = 1$

e. q. of a circle ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

${(x - 4)}^{2} + {(y + 2)}^{2} = 1^{2}$

$x^{2} + y^{2} - 8 x + 4 y + 19 = 0$

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