Question

The set of values of p for which the power of a point $(2,5)$ is negative with respect to a circle $x^2+y^2-8x-12y+p=0$ which neither touches the axes nor cuts them are

• A. (36,57)
• B. (36,47)
• C. (37,47)
• D. (16,47)

Answer 1

The correct option is B (36,47)

Power is negative $\Rightarrow S_1<0$

$\Rightarrow 2^2+5^2-16-60+p<0$

$\Rightarrow 4+25-76+p<0$

$\Rightarrow p<47$

& square of x-coordinate of circle's

centre > square of radius (does not cut axes)

$\Rightarrow g^2>g^2+f^2-c$

$\Rightarrow f^2-c<0\Rightarrow f^2<C$

$\Rightarrow 36<p$ similarly $g^2<c$

$\Rightarrow 16<p\Rightarrow p>36$

$\Rightarrow p\in (36,47)$