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Question

If circle x2+y26x10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is

A
(6,25)
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B
(6,29)
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C
(25,29)
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D
R(6,25)
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Solution

The correct option is C (25,29)
Given circle S:x2+y26x10y+c=0
(1,4) lies inside of the given circle
S1<012+42610(4)+c<0c<29(1)
Circle will not meet the xaxis if g2c<0
c>9(2)
Circle will not meet the yaxis if f2c<0
c>25(3)
From (1),(2),(3) we get
c(25,29)

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