Answer:
a) 15 units
b) [tex]f(x) = (x-12)^2 + (x-15)^2 + (x-15)^2 - 225\\\\[/tex]
Step-by-step explanation:
Part a
x-y plane z = 0
The distance from a point to plane:
[tex]d = \frac{Ax_{0} + By_{0} + Cz_{0} + D }{\sqrt{A^2 + B^2+C^2} } \\\\d = \frac{0*12 + 0*15 + 1*15 + 0 }{\sqrt{0 + 0+1^2} }\\\\d = 15 units[/tex]
Part b
[tex]f(x) = (x-a)^2 + (x-b)^2 + (x-c)^2 - R^2\\\\[/tex]
Where,
a = 12
b = 15
c = 15
[tex]f(x) = (x-12)^2 + (x-15)^2 + (x-15)^2 - (15)^2\\\\[/tex]
[tex]f(x) = (x-12)^2 + (x-15)^2 + (x-15)^2 - 225\\\\[/tex]
