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

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Q. If $P (2,8)$ is an interior point of a circle $x ^{2}+ y ^{2}-2 x +$ $4 y-p=0$ which neither touches nor intersects the axes, then set for $p$ is

Conic Sections

Solution:

For internal point $ p (2,8) 4+64-4+32- p <0$
$ \Rightarrow p >96$ and $x $ intercept $=2 \sqrt{1+ p }$ therefore, $ 1+ p <0 $
$ \Rightarrow p <-1$ and $ y $ intercept $=2 \sqrt{4+ p } $
$\Rightarrow p <-4$