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Question

If P(2,8) is an interior point of a circle x2+y2−2x+4y−p=0 which neither touches nor intersects the axes, then set for p is -

A
p<1
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B
p<4
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C
p>96
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D
pϕ
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Solution

The correct option is D pϕ
Since the point P is interior to the circle, S1 < 0
=(22)+(82)2.(2)+4(8)p<0
=96p<0
=p>96
Also given that the circle doesn't touches any of the axes.
So, g2c < 0
f2c < 0
g2c < 0
=1+p<0
=p<1
Also,
f2c < 0
=4+p<0
=p<4
Since p<4 and p>96 is not possible, the set for p will be a null set meaning it'll not have any element in it.

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