Question

if the point p(x,y) is equidistant from a points A(a+b,b-a) an B(a-b ,b+a).prove that bx = ay.

i don't need copied answer...

Answer 1

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Answer 2

If point P ( x, y) is equidistant from A and B, then the distance between them will be equal.

PA = PB

√[ ( a + b) - x ] ^2 + [( b - a ) - y ] ^2 =√ [( a - b ) - x] ^2 + ( b + a - y ) ^2

( a + b - x ) ^2 + ( b - a - y ) ^2 = ( a - b - x ) ^2 + ( a + b - y) ^2

( a + b - x ) ^2 - ( a - b - x ) ^2 = ( a +b - y ) ^2 - ( b - a - y ) ^2

( a +b - x + a - b - x ) ( a +b - x - a +b +x ) = ( a +b - y + b - a - y ) ( a +b - y - b + a +y )

( 2a - 2x) ( 2b) = ( 2b - 2y ) ( 2a )

2 [( a - x ) b] = 2 [( b - y ) a ]

(a - x ) b = ( b - y) a

ab - xb = ab - ay

$<h3>ay = bx$

Hence, PROVED.