1. Tardigrade
  2. Question
  3. Mathematics
  4. The set of values of p for which the power of a point (2,5) is negative with respect to a circle x2+y2-8 x-12 y+p=0 which neither touches the axes nor cuts them are

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Conic Sections

Solution:

$x^2+y^2-8 x-12 y+p=0$
Power of $(2,5)$ is $S_1=4+25-16-60+P=P-47<0 \Rightarrow P<47$
Circle neither touches nor cuts coordinate axes
$g^2-c<0 \Rightarrow 16-p<0 \Rightarrow p>16$
$f^2-c<0 \Rightarrow 36-p<0 \Rightarrow p>36$
taking intersection $P \in(36,47)$