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Analytical Geometry

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Joined:	6 Apr 2007
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27 Oct 2007 19:26:33 IST

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iit problem(circles)

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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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ameya sahasrabudhe

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Joined: 17 Jul 2007

Posts: 252

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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