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The circle \mathrm{x^2+y^2-6 x-10 y+k=0} does not touch or intersect the co-ordinate axes and the point (1,4) is inside the circle. Then the range of the values of k is.

Option: 1

(25,29)


Option: 2

(29,34)


Option: 3

(20,29)


Option: 4

(29,47)


Answers (1)

best_answer

\mathrm{S: x^2+y^2-6 x-10 y+k=0}.
Centre \mathrm{C(3,5), r^2=9+25-k=34-k}.
Point P(1,4) lies inside the circle.
\mathrm{ \therefore \quad S^{\prime}=- \text { ive } \Rightarrow-29+k<0 \text { or } k<29 }    .....(i)
Since the circle neither touches nor intersects the axes of coordinates, therefore from the figure it is clear that r < 3 ( x coordinate of centre) and r < 5 (y coordinate of centre).

Hence, \mathrm{ r<3 \Rightarrow r^2<9 }
\mathrm{ \Rightarrow 34-k<9 \Rightarrow 25>k }    .....(ii)
From (i) and (ii), we have 25 < k < 29.

Posted by

shivangi.bhatnagar

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