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Show that the point (x ,y) given by x=(2...

Show that the point `(x ,y)` given by `x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1+t^2))` lies on a circle for all real values of `t` such that `-1lt=tlt=1,` where a is any given real number.

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To show that the point \((x, y)\) given by \[ x = \frac{2a t}{1 + t^2}, \quad y = \frac{1 - t^2}{1 + t^2} \] lies on a circle for all real values of \(t\) such that \(-1 \leq t \leq 1\), where \(a\) is any given real number, we will follow these steps: ...
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