Find the radius of the circle in which the sphere x2+ text y2+ text z2+2x-2y-4z=19 is cut by the plane x+2y+2z+7=0 .

Question

Find the radius of the circle in which the sphere x2+ text y2+ text z2+2x-2y-4z=19 is cut by the plane x+2y+2z+7=0 . (A)  2  (B)  3  (C)  1  (D)  4

Tardigrade Admin · Accepted Answer

Given equation of sphere is x2+y2+z2+2x-2y-4z-19=0 ?.(i) Its centre =(-1,1,2), radius =√1+1+4+19 =√25=5 and equation f plane is x+2y+2z+7=0 ?.(ii) Length of the perpendicular from point (-1, 1, 2) to the plane (ii) is | (-1+2+4+7/√1+4+4) |=(12/3)=4 ∴ Radius of circle =√(5)2-(4)2=√25-16=3

Q. Find the radius of the circle in which the sphere $x^{2} + y^{2} + z^{2} + 2 x - 2 y - 4 z = 19$ is cut by the plane $x + 2 y + 2 z + 7 = 0$ .

$2$

$3$

$1$

$4$

Q. Find the radius of the circle in which the sphere x2+y2+z2+2x−2y−4z=19 is cut by the plane x+2y+2z+7=0 .

2

3

1

4

Q. Find the radius of the circle in which the sphere $x^{2} + y^{2} + z^{2} + 2 x - 2 y - 4 z = 19$ is cut by the plane $x + 2 y + 2 z + 7 = 0$ .

$2$

$3$

$1$

$4$