Question

A(2, 4) and B(5, 8), find the equation of
the locus of point P such that
PA^2 - PB^2 = 13.

​

Answer 1

Answer:

6x+8y-82=0

Step-by-step explanation:

Using Distance formula.

Answer 2

6x + 8y  = 82 is  the equation of the locus of point P such that PA² - PB²  = 13 where A(2, 4) and B(5, 8)

Step-by-step explanation:

Let say P = (x , y)

A(2, 4) and B(5, 8)

PA²  = (x - 2)² + (y - 4)²

PB² = (x - 5)²  + (y - 8)²

PA² - PB²  = 13

=>  (x - 2)² + (y - 4)²  -  ( (x - 5)²  + (y - 8)²)  = 13

=> ( x² + 4 - 4x  + y² + 16 - 8y)  - (x² + 25 - 10x  + y² + 64 - 16y) = 13

=> 6x + 8y  + 20 - 89 = 13

=> 6x + 8y  = 82

6x + 8y  = 82 is  the equation of the locus of point P

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