Drawing a diagram showing how a parabola is generated

I need help. How do I create a plot like the one shown below in Wolfram Mathematica?

It's the upper-right picture, for value of p = 1/2, that I want. Is it possible at all? • – kglr Jan 16 at 22:04

ClearAll[f];
f[F_, y_] = x /. Solve[x^2 == (x - F)^2 + y^2, x][]
Manipulate[
Show[
ParametricPlot[{f[F, y], y}, {y, -6, 6}],

Graphics[{
Point[{f[F, y], y}], Text["M", {f[F, y], y} + 0.25],
Point[{F, 0}], Text["F", {F, 0} + 0.25],
Point[{0, y}], Text["A", {0, y} + 0.25],
Line[{{0, y}, {f[F, y], y}}],
Line[{{F, 0}, {f[F, y], y}}]

}],
Axes -> True, PlotRange -> {{-10, 10}, {-6, 6}},
AxesOrigin -> {0, 0},
ImageSize -> Large
],
{{y, 1}, -6, 6}, {{F, 1}, -10, 10}
] • Just for the giggles I fiddled this up: wolfr.am/AFSiGUta – b3m2a1 Jan 16 at 21:46
• Thank you! This rocks! :) – Danica Jan 16 at 21:48
• You're welcome! (I hope you've tried the sliders...) – Henrik Schumacher Jan 16 at 21:49

Just reverse your coordinates:

standardParabola[x_] := (x^2);
ListLinePlot[
Table[Evaluate@{standardParabola[x], x}, {x, -5, 5, .01}]
]

Try this online

• Tnx for help! :) – Danica Jan 16 at 21:51
Plot[{Sqrt[x], -Sqrt[x]}, {x, -2, 4},
PlotStyle -> {Blue, Blue},
Epilog -> {Green, Thickness[0.005], Line[{{-1, -2}, {-1, 2}}],
Red, PointSize[0.02], Point[{1, 0}],
Dashed, Line[{{1, 0}, {.25, .5}, {-1, .5}}]}] I deliberately placed the locations of the points and lines incorrectly. It is your job to get them right!

• Thank you so much. It's more than enough. :) – Danica Jan 16 at 21:48