Find equations of the spheres with center(1, −1, 6)that touch the following planes. a) xy-planeb) yz-planec) xz-plane

Given :

Center of sphere , C( 1 , -1 , 6 ) .

To Find :

Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .

Solution :

a)

Distance of the point from xy-plane is :

d = 6 units .

So , equation of circle with center C and radius 6 units is :

b)

Distance of point from yz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

c)

Distance of point from xz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

Hence , this is the required solution .

step-by-step explanation: