Question

1. If point \( P \) is at equal distance 5 from \( A \equiv(a+b, b-a) \) and \( B \equiv(a-b, a+b) \) then locus of \( P \) is - (1) \( a x=b y \) (2) \( b x=a y \) (3) \( a x+b y=0 \) (4) \( b x+a y=0 \)

Answer 1

A ≡ ( a + b , b − a )  and B ≡ ( a − b , a + b ) 

let P be ( x,y )

PA = PB

{x -( a+b) }²  + {y -( b-a) }²  = {x -( a-b) }²  + {y -( a+b)) }² 

{x -( a+b) }²  -  {x -( a-b) }² = {y -( a+b)) }²  - {y -( b-a) }²

[ 2x - 2a ] [ x - a - b - x + a - b ] = [ 2y - 2b ] [ y -a -b -y + b - a ]

[ x - a ] [ -2b]  = [ y - b ] [ - 2a]

-bx + ba = - ay + ab

ay = bx