# 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

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 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