11 Find an equation for the set of all points that are equid

(11) Find an equation for the set of all points that are equidistant from the points (2, 1, 0) and (4, 0, 3). Describe this surface. Show all work.

Given pts are (-2,1,0) & (4,0,3)

According to the given condition, we have

(x+2)²+(y-1)²+z²= (x-4)²+(y-0)²+(z-3)²

x²+4+4x+y²+1-2y+z²=x²+16-8x+y²+z²+9-6z

4x-2y+5= 25-8x-6z

12x-2y+6z=20

2(6x-y+3z)=20

6x-y+3z=10 which is of the form AX+BY+CZ=D i.e this is the equation of the plane.