Answer
Equations of the spheres with center (2, -3 6) that touch
(a) the XY-plane is (x-2)^2 + ( y+ 3)^2 + ( z- 6)^2 =36.
(b) the yz-plane is (x- 2)^2 + (y+ 3)^2 + (z- 6)^2 = 4.
(c) the xz-plane is (x- 2)^2 + (y+ 3)^2 + (z- 6)^2 = 9.
Work Step by Step
(a)
Since the sphere touches the XY plane, its radius is the distance from its center, (2, -3, 6), to the XY plane, namely 6.Therefore r = 6 and an equation of the sphere is (x-2)^2 + ( y+ 3)^2 + ( z- 6)^2 =36.
(b)
Since the sphere touches theyz- plane, its radius is the distance from its center (2, -3, 6) to the yz-plane, which is 2. Therefore r = 2 and an equation is (x- 2)^2 + (y+ 3)^2 + (z- 6)^2 = 4.
(C)
Since the sphere touches the xz-plane, its radius is the distance from its center (2, -3, 6) to the xz-plane, which is 3. Therefore r = 3 and an equation is (x- 2)^2 + (y+ 3)^2 + (z- 6)^2 = 9.
