If points $$A(3$$,$$5)$$ and B are equidistant from $$H(2$$,$$5)$$ and B has rational coordinates, then $$AB=$$

Correct option is 4None of these

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If points A(3,5) and B are equidistant from $H (\sqrt{2}, \sqrt{5})$ and B has rational coordinates, then AB=

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(3−2)2+(5−5)2

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Correct option is D

Let B≡(α,β), where α,β are rational. Given HA2=HB2⇒(3−2)2+(5−5)2=(α−2)2+(β−5)2⇒41−62−105=α2+β2+7−22α−25β⇒α2+β2−34+2(3−α)2+2(5−β)5=0Since α and βare rational, 5−β=0⇒β=5and3−α=0⇒α=3∴AB=0

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If points A(3,5) and B are equidistant from H(2,5) and B has rational coordinates, then AB=

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If points A(3,5) and B are equidistant from $H (\sqrt{2}, \sqrt{5})$ and B has rational coordinates, then AB=