Question

If $(2,5)$ is an interior point of the circle $x^2+y^2-8x-12y+p=0$ and the circle neither cuts nor touches any one of the axes of coordinates then

• A. $pϵ(36,47)$
• B. $pϵ(16,47)$
• C. $pϵ(16,36)$
• D. None of these

Answer 1

Answer: (A)

$pϵ(36,47)$

$\because$ Point $(2,5)$ lies in interior of the given circle,
$\Rightarrow 4+25-16-60+P<0$
$\Rightarrow P-47<0\Rightarrow P<47..\left(1\right)$
Also radius $<x$ and $y$ corordinate of centre
$\Rightarrow \sqrt{16+36-P}<4$ and $6$
$\Rightarrow \sqrt{52-P}<4$ and $6$
$\Rightarrow 52-P<16$ and $36$
$\Rightarrow -P>-36$ and $-16$
$\Rightarrow P>36$ and $16..\left(2\right)$
Combining (1) and (2) we get,
$\therefore P\in (36,47)$