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Writing:

r = 1;
tt = 2 ArcTan[3 - 2 Sqrt[2]];

x = r Cos[t];
y = r Sin[t];

a = -1/(2 r Sin[tt]);
b = 0;
c = 5/3 r;

ParametricPlot[{{x, y}, {x, a x^2 + b x + c}}, 
                {t, -Pi - tt, tt}, 
                AxesLabel -> {"x", "y"}]

I get:

enter image description here

but I do not understand why the two graphs do not link up! Ideas?

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Endpoints of the expressions are equal, but a x^2 + b x + c makes an overshot.

{{x, y}, {x, a x^2 + b x + c}} /. t -> -Pi - tt // N

(*   {{-0.942809, 0.333333}, {-0.942809, 0.333333}}   *)

{{x, y}, {x, a x^2 + b x + c}} /. t -> tt // N

(*   {{0.942809, 0.333333}, {0.942809, 0.333333}}   *)

Plot[{y, a x^2 + b x + c}, {t, -Pi - tt, tt}, 
   PlotStyle -> {Red, Blue}]

enter image description here

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  • $\begingroup$ Thanks so much! $\endgroup$ – TeM May 11 '18 at 11:29

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