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

Question

If P (2,8) is an interior point of a circle x 2+ y 2-2 x + 4 y-p=0 which neither touches nor intersects the axes, then set for p is (A) p <-1 (B) P<-4 (C) p >96 (D) φ

Tardigrade Admin · Accepted Answer

For internal point p (2,8) 4+64-4+32- p <0 ⇒ p >96 and x intercept =2 √1+ p therefore, 1+ p <0 ⇒ p <-1 and y intercept =2 √4+ p ⇒ p <-4

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

$p < - 1$

$P < - 4$

$p > 96$

$ϕ$

For internal point $p (2, 8) 4 + 64 - 4 + 32 - p < 0$
$\Rightarrow p > 96$ and $x$ intercept $= 2 1 + p$ therefore, $1 + p < 0$
$\Rightarrow p < - 1$ and $y$ intercept $= 2 4 + p$
$\Rightarrow p < - 4$

Q. If P(2,8) is an interior point of a circle x2+y2−2x+ 4y−p=0 which neither touches nor intersects the axes, then set for p is

p<−1

P<−4

p>96

ϕ

For internal point p(2,8)4+64−4+32−p<0 ⇒p>96 and x intercept =21+p​ therefore, 1+p<0 ⇒p<−1 and y intercept =24+p​ ⇒p<−4

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

$p < - 1$

$P < - 4$

$p > 96$

$ϕ$

For internal point $p (2, 8) 4 + 64 - 4 + 32 - p < 0$
$\Rightarrow p > 96$ and $x$ intercept $= 2 1 + p$ therefore, $1 + p < 0$
$\Rightarrow p < - 1$ and $y$ intercept $= 2 4 + p$
$\Rightarrow p < - 4$