Show that the point (x, y) given by x=2at1+t2 and y=a1-t21+t2 lies on – InterviewSolution

1.	Show that the point (x, y) given by x=2at1+t2 and y=a1-t21+t2 lies on a circle for all real values of t such that -1≤t≤1, where a is any given real number. [NCERT EXEMPLAR]
Answer» Show that the point (x, y) given by $x = \frac{2 a t}{1 + t^{2}}$ and $y = a (\frac{1 - t^{2}}{1 + t^{2}})$ lies on a circle for all real values of t such that $- 1 \leq t \leq 1$ , where a is any given real number. [NCERT EXEMPLAR]

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