Any software recommendations to draw such graphs?

Question

I am looking any alternatives software to draw similar graph images i posted here.

Answer 1

If you are looking to graph for the sake of graphing, then Desmos is probably the way to go. You can see a demo of the graph you want here. If you want to graph this for publication, then Tikz in LaTeX is your best bet. Something like this would be a starting point:

\begin{tikzpicture}[scale = 2]
\draw[->] (-1.2,0) -- (1.5,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,1.5) node[above] {$y$};
\draw[smooth, samples = 100, domain = -1.2:1.2] plot(\x,{\x*\x});
\draw[smooth, samples = 100, domain = -1.2:1.2,variable = \y] plot({\y*\y},\y);
\draw (-.5,.8) node {$x^2 = 2py$};
\draw (.8,-.5) node {$y^2 = 2px$};
\draw (1.3,.9) node {$(2p,2p)$};
\end{tikzpicture}

Answer 2

Asymptote, deeply integrated with LaTeX.

settings.tex="pdflatex";
import graph;
size(6cm);
import fontsize;defaultpen(fontsize(9pt));
texpreamble("\usepackage{lmodern}\usepackage{amsmath}"
            +"\usepackage{amsfonts}\usepackage{amssymb}");
pen linePen=darkblue+0.7bp;
real p=2;
real xmin=-2p-0.1,xmax=2p+0.1;
real ymin=-2p-0.1,ymax=2p+0.1;
real dxmin=0, dxmax=0.22;
real dymin=dxmin, dymax=dxmax;
xaxis("$x$",xmin-dxmin,xmax+dxmax,RightTicks(Step=1,step=0.5,OmitTick(0)),above=true);
yaxis("$y$",ymin-dymin,ymax+dymax,LeftTicks (Step=1,step=0.5,OmitTick(0)),above=true);
typedef pair pairFreal(real);
pairFreal Fy(real p){return new pair(real x){return (x,x^2/2/p);};}
pairFreal Fx(real p){return new pair(real y){return (y^2/2/p,y);};}
guide gy=graph(Fy(p),xmin,xmax);
guide gx=graph(Fx(p),ymin,ymax);
guide ga=graph(Fy(p),0,2p)--reverse(graph(Fx(p),0,2p))--cycle;
fill(ga,paleblue);
draw(gy^^gx,linePen);
dot("$(2p,2p)$",(2p,2p),plain.NW,UnFill);
label("$x^2=2py$",Fy(p)(-1.5p),plain.NE);
label("$y^2=2px$",Fx(p)(-1.5p),plain.NE);
shipout(bbox(Fill(paleyellow)));