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

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

Tardigrade Admin · Accepted Answer

x2+y2-8 x-12 y+p=0 Power of (2,5) is S1=4+25-16-60+P=P-47<0 ⇒ P<47 Circle neither touches nor cuts coordinate axes g2-c<0 ⇒ 16-p<0 ⇒ p>16 f2-c<0 ⇒ 36-p<0 ⇒ p>36 taking intersection P ∈(36,47)

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

$(36, 57)$

$(36, 47)$

$(37, 47)$

$(16, 47)$

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

(36,57)

(36,47)

(37,47)

(16,47)

x2+y2−8x−12y+p=0 Power of (2,5) is S1​=4+25−16−60+P=P−47<0⇒P<47 Circle neither touches nor cuts coordinate axes g2−c<0⇒16−p<0⇒p>16 f2−c<0⇒36−p<0⇒p>36 taking intersection P∈(36,47)

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

$(36, 57)$

$(36, 47)$

$(37, 47)$

$(16, 47)$