Answer:
Step-by-step explanation:
To find the equation of a sphere with center (2,-3,6) that touch
(a) the xy-plane,
The equation of xy plane is z=0
Hence the radius would be distance from z=0 perpendicular to xy plane = z coordinate =6
Equation is
[tex](x-2)^2+(y+3)^2+(z-6)^2 =36[/tex]
(b) the yz-plane,
The equation of yz plane is x=0
Hence the radius would be distance from x=0 perpendicular to yz plane = x coordinate =2
Equation is
[tex](x-2)^2+(y+3)^2+(z-6)^2 =4[/tex]
(c) the xz-plane.
The equation of zx plane is y=0
Hence the radius would be distance from y=0 perpendicular to zx plane = |y coordinate| =3
Equation is
[tex](x-2)^2+(y+3)^2+(z-6)^2 =9[/tex]
