Find the locus of P if PA 2 + PB 2 = 2k 2 where A and B are the points (3,4,5) and (-1,3,-7).

Let P(x,y,z) be the point whose locus is to be found, Now PA 2 + PB 2 = 2k 2 . (x - 3) 2 + (y - 4) 2 + (z - 5) 2 + (x + 1) 2 + (y - 3) 2 + (z + 7) 2 =2k 2 x 2 - 6x + 9 + y 2 - 8y + 16 + z 2 - 10z + 25 + x 2 + 2x + 1 + y 2 - 6y + 9 + z 2 + 14z + 49 = 2k 2 2x 2 + 2y 2 + 2z 2 - 4x - 14y + 4z + 109 = 2k 2 .

1800-212-7858 (Toll Free)

9:00am - 8:00pm IST all days

8104911739

For Business Enquiry

Customer Support

Home / Doubts and Solutions/CBSE/Class 11 Science/Mathematics

Find the locus of P if PA² + PB² = 2k² where A and B are the points (3,4,5) and (-1,3,-7).

Asked by Topperlearning User 20th February 2015, 10:30 AM

Answered by Expert

Answer:

Let P(x,y,z) be the point whose locus is to be found, Now

PA² + PB² = 2k².

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

x² - 6x + 9 + y² - 8y + 16 + z² - 10z + 25 + x² + 2x + 1 + y² - 6y + 9 + z² + 14z + 49 = 2k²

2x² + 2y² + 2z² - 4x - 14y + 4z + 109 = 2k².