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Question

If the power of point (2,1) with respect to the circle 2x2+2y28x6y+k=0 is positive, then

A
12<k<
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B
12<k<12
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C
12<k<252
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D
12<k<25
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Solution

The correct option is C 12<k<252
2x2+2y28x6y+k=0
x2+y24x3y+k2=0
Radius =4+94k2=252k4
Clearly, 252k4>0
k<252 (1)

The power of the point (2,1) with respect to the circle 2x2+2y28x6y+k=0 is
S1=2(2)2+2(1)28(2)6(1)+k
S1=12+k
Given S1>0
Then 12+k>0
k>12 (2)

From (1) and (2),
12<k<252

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