Afunction[r_, x_, y_] := -x/r + (y^2 - 1)/(2 r^2)

Acurve[x_, y_] := Plot[{Afunction[r, x, y], (x^2 - 1)/2}, {r, 0, 10}, PlotRange -> {{0, 10}, {-1.5, 1.5}}]

someInfo[x_, y_] := If[(0 < x < 1 && y > 1), Text[Style[StringJoin["Just a test :nn", "r = ", ToString[NumberForm[x/(1 - x^2), {5, 4}]], " km"]], {5, -1.25}], {}]

Manipulate[Show[Acurve[x, y],
PlotRange -> {{0, 10}, {-1.5, 1.5}},
AspectRatio -> 1,
Frame -> True,
Epilog -> someInfo[x, y]],

Row[{
    Control[{{x, 0.8}, -1, 2, 0.001, Appearance -> {"Labeled"}}],
    Spacer[124],
    Control[{{y, 1.5}, 0, 15, Appearance -> {"Labeled"}}]
}]]