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If P (2,8) is an interior of a circle x 2 + y 2 + 4y – p = 0 which neither touches nor intersects the axes, then set for p is - (a) p (b) P (c) p > 96 (d) f


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


        (a)    p < - 1


(b)    P < - 4


(c)    p > 96


(d)    f


Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Equation of circle:
x^{2}+(y+2)^{2} = (\sqrt{p+4})^{2}
p+4> 0
\Rightarrow p> -4...........(1)
P(2, 8) is interior to the circle
2^{2}+8^{2}+4.8-p< 0
\Rightarrow p> 100
If there is no condition on touching or intersexting the x- axis, then
\Rightarrow p> 100
If circle is not touching & intersecting the x-axis, we have
0< \sqrt{p+4}< 2
-4< p< 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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