If the point (1, 4) lies inside the circle x2 + y2 — 6x-10y + p = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval:

Question

If the point (1, 4) lies inside the circle x2 + y2 — 6x-10y + p = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval: (A) (0, 25) (B) (25, 39) (C) (9, 25) (D) (25, 29)

Tardigrade Admin · Accepted Answer

AB=√22+1=√5 according to question √5<√32+52-p< q 5 < 34 - p < q - 29 < - P < - 25 29 > p > 25

Q. If the point (1, 4) lies inside the circle $x^{2} + y^{2} —6 x - 10 y + p = 0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $p$ is the interval:

(0, 25)

(25, 39)

(9, 25)

(25, 29)

$A B = 2^{2} + 1 = 5$
according to question
$5 < 3^{2} + 5^{2} - p < q$
$5 < 34 - p < q$
$- 29 < - P < - 25$
$29 > p > 25$

Q. If the point (1, 4) lies inside the circle x2+y2—6x−10y+p=0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval: