Question:
3.If A and B are the points ( 1, 2, 3 ) and ( -1, 4 , -3) respectively then find the locus of a point P such that PA2 - PB2 = 2k2
Answer:
Given A and B are the points (1, 2, 3) and (-1, 4, -3) respectively.
Let point of P is (x, y, z)
Again given PA2 - PB2 = 2k2
=> {(x - 1)2 + (y - 2)2 + (z - 3)2 } - {(x + 1)2 + (y - 4)2 + (z + 3)2 } = 2k2
=> {x2 + 1 - 2x + y2 + 4 - 4y + z2 + 9 - 6z} - {x2 + 1 + 2x + y2 + 16 - 8y + z2 + 9 + 6z} = 2k2
=> {-2x + 4 - 4y - 6z} - {2x + 16 - 8y + 6z} = 2k2
=> -2x + 4 - 4y - 6z - 2x - 16 + 8y - 6z = 2k2
=> -4x + 4y - 12z - 12 - 2k2 = 0
=> 2x - 2y + 6z + 6 + k2 = 0
Not what you are looking for? Go ahead and submit the question, we will get back to you.
