Question

Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane

(i)C(-2,4,-6)

Answer 1

(a)

Since the sphere touches the xy-plane, its radius is the distance from its center, $(-2, 4, -6),$ to the xy-plane, which is $6.$ Therefore $r = 6$ and an equation of the sphere is

$$(x+2)^2+(y-4)^2+(z+6)^2=36$$

(b)

Since the sphere touches the xz-plane, its radius is the distance from its center, $(-2, 4, -6),$ to the xz-plane, which is $4.$ Therefore $r = 4$ and an equation of the sphere is

$$(x+2)^2+(y-4)^2+(z+6)^2=16$$

(c)

Since the sphere touches the yz-plane, its radius is the distance from its center, $(-2, 4, -6),$ to the yz-plane, which is $2.$ Therefore $r = 2$ and an equation of the sphere is

$$(x+2)^2+(y-4)^2+(z+6)^2=4$$