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If the point (1,4) lies inside the circle $x^{2} + y^{2} - 6 x - 10 y + p = 0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval

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(0,25)

(9,25)

(25,29)

(25,39)

answer is D.

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Detailed Solution

$c = (3, 5) r = \sqrt{34 - p} \to \sqrt{34 - p} < 3 \Rightarrow p > 25.$

$s_{11} < 0 \Rightarrow p < 29$

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