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A rod $A B$ of length $4$ units moves horizontally with its left end $A$ always on the circle $x^{2} + y^{2} - 4 x - 18 y - 29 = 0$ then the locus of the other end $B$ is

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$x^{2} + y^{2} - 4 x - 8 y - 29 = 0$

$x^{2} + y^{2} - 12 x - 18 y + 3 = 0$

$x^{2} + y^{2} - 12 x - 8 y + 3 = 0$

$x^{2} + y^{2} - 4 x - 16 y + 19 = 0$

answer is B.

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Detailed Solution

$x = x - 4 {(x - 4)}^{2} + y^{2} - 4 (x - 4) - 18 y - 29 = 0 x^{2} + y^{2} - 12 x - 18 y + 3 = 0$

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