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Question

Show that, if x2+y2=1, then the point (x2+y2,1x2y2) is at a distance 1 unit from the origin.

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Solution

Given x2+y2=1.
Now the distance of the point (x2+y2,1x2y2) from the origin is:
(x2+y20)2+(1x2y20)2=x2+y2+1x2y2=1.
Hence, Proved.

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