Question

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

• A. $p<–1$
• B. $p<–2$
• C. $p>2$
• D. $\varphi$

Answer 1

The correct option is B $p<–2$

For internal point $P(2,8)$

$4+64-8+32-p<0$

$\Rightarrow p>92$ and $x-$ intercept$=2\sqrt{1+p}$

$\therefore 1+p<0$

$\Rightarrow p<-1$ and $y-$ intercept=2\sqrt{2+p}$

$\Rightarrow p<-2$