Question

find the focus of the point which is equidistant from (1,2,3) and (3,2,-1)​

Answer 1

Step-by-step explanation:

Let the unknown point be P(x, y, z)

Given that PA=PB

=>PA^2=PB^2

Thus, we can write

$(x - 1) {}^{2} + (y - 2) {}^{2} + (z - 3) {}^{2} = (x - 3) {}^{2} + (y - 2) {}^{2} + (z + 1) {}^{2} \\ x {}^{2} - 2x + 1 + y {}^{2} - 4y + 4 + z {}^{2} - 6z + 9 = x {}^{2} - 6x + 9 + y {}^{2} - 4y + 4 + z {}^{2} + 2z + 1 \\ 4x - 8z = 0$

That is the required equation