.. If the points (x, y) is equidistant from (a,0)
and (2a, a) then show that x + y - 2a=0.
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Step-by-step explanation:
(x, y) is equidistant from (a,0) and (2a, a)
=> (a-x)²+(0-y)² = (2a-x)²+(a-y)²
=> a²-2ax+x²+y² = 4a²-2(2a)(x)+x²+a²-2ay+y²
=> -2ax = 4a²-4ax-2ay
=> 4a²-4ax-2ay+2ax = 0
=> 4a²-2ax-2ay = 0
=> 2a ( 2a-x-y) = 0
=> 2a-x-y = 0
=> -(2a-x-y) = -(0)
=> x+y-2a = 0 , which is the require equation
Hence proved
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