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Question

The circle x2+y2=16 is cut by line x+y=2, then (5+r2,3+r2) lies in the major segment if r belongs to

A
(4214,42+14)
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B
(,52)
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C
(4214,52)
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D
(0,1)
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Solution

The correct option is C (4214,52)
Given: (5+r2,3+r2) lies in the major segment.
Then, (0,0) and (5+r2,3+r2) are along same side of x+y=2.

(5+r23+n22)2>0

102r>0

r<52 ----(1)

and (5+r2,3+r2 lies inside circle x2+y2=16
(5+r1,3+r216<0
2×r22+3452r32r16<0
r282r+18<0
r+[42414,52]----(2)
From (1) & (2)
r+[4214,52]

57945_33484_ans.png

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