Question

Find the equation of set of points P Such that PA²+ PB ² = 2K² where A&B are the points (3,4,5) & (-1,3,-7) respetively

Answer 1

Answer:

Let P = (x,y,z),B = (3,4,5) and B = (-1,3-7).

Now, PB² = (x +1)² + (y – 3)² + (z + 7)²

and

PA² = (x – 3)² + (y – 4)² + (z – 5)²

Given that PA² + PB² = 2k², then

(x - 3)² + (y - 4)² +(z - 5)² + (x + 1)² +(y - 3)² + (z + 7)² = 2k²

⇒ x² – 6² + 9 + y² – 8y + 16 + z² – 10z +

22 + x² + 2x +1 + y² – 6y + 9 + z² +14z +

49 = 2k.

⇒ 2x² + 2y² + 2z² – 4x – 14y + 4z + 109

= 2k²

⇒ 2x² + 2y² + 2z² – Ax – 14y + 4z = 2k² -109

Hope this helps you...