Question

Which tower/s transmit the calls to phone located at (a) (-4, 2), (b)
(2, 0) and (c) (4, 10)?

Answer 1

Answer:

Let P(x,y,z) be the point that is equidistant from points A(1,2,3) and B(3,2,−1) .

i.e. PA=PB

⇒PA

2

=PB

2

⇒(x−1)

2

+(y−2)

2

+(z−3)

2

=(x−3)

2

+(y−2)

2

+(z+1)

2

⇒x

2

−2x+1+y

2

−4y+4+z

2

−6z+9=x

2

−6x+9+y

2

−4y+4+z

2

+2z+1

⇒−2x−6z+14=−6x+2z+14

⇒−2x−6z+6x−2z=0

⇒4x−8z=0

⇒x−2z=0

Thus the required equation is x−2z=0.

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