Question

A and B be the points (3,4,5) and (-1,3,-7), respectively, find the equation of the
set of points P such that PA + PB =k, where k is a constant.
k +1
k+ 1k+1
rythe​

Answer 1

Answer:

Let point P ≡ (x , y, z )

A/C to question,

(PA)² + (PB)² = K²

use distance formula ,

PA² = (x - 3)² + (y -4)² + (z - 5)²

PB² = (x + 1)² + (y - 3)² + (z + 7)²

Now,

(x - 3)² + (y - 4)² + (z - 5)² + (x + 1)² + (y - 3)² + (z + 7)² = K²

{(x - 3)² + (x + 1)² } + {(y -4)² + (y - 3)²} + {(z - 5)² + (z + 7)²} = K²

{(2x² -4x + 10} + { 2y² - 14y + 25 } + {2z² +4z + 74 } = K²

2(x² + y² + z²) +( -4x - 14y + 4z) + (10 + 25 + 74) = K²

2(x² + y² + z²) -4x - 14y + 4z + 109 - k² = 0

Which is required equation .

hope it helps

tq.......////

Step-by-step explanation: