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![[Post New]](/templates/default/images/icon_minipost_new.gif) 27 Oct 2007 19:26:33 IST
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Q. A circle has its centre (0,root2). Prove that at the most two rational points can lie on the circle.
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28 Oct 2007 01:42:34 IST
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look, sachin
we first write the eqn to circle in parametric form.
x=rcos@ y=root2+rsin@
a point is rational if both its coordinates are rational.
here, @ can vary from 0 to 2 pie.
so, sin@ becomes negative twice.
thus, we have only two points( at most) where both coordinates cud be rational.
hence proved
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