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

$(a)\;(0,25) \qquad(b)\;(25,39)\qquad(c)\;(9,25)\qquad(d)\;(25,29)$

Can you answer this question?

Since centre of circle (3,5)
To not touch coordinate axis, radius of circle> 3
Gives P>25

Also 1,4 lies inside gives S_1<0   at(1,4)
Gives P<29
answered Apr 2, 2015