You can alternatively use Graphics
with the primitive Disk
.
Definitions.
disk = {Darker[Gray, 0.5], Disk[{0, 0}, 20]};
frame = {{Automatic, None}, {Automatic, None}};
plotrange = {{-50, 50}, {-50, 50}};
gridlines = ConstantArray[
Join[
(* all lines *)
{#, Directive[LightGray, Thin]} & /@ Range[-50, 50, 2],
(* main lines *)
{#, Directive[Lighter[Black, 0.5]]} & /@ Range[-40, 40, 20]],
2
];
labelstyle = Directive[Black, FontSize -> 18];
Graphics.
Graphics[disk,
Frame -> frame, PlotRange -> plotrange, GridLines -> gridlines,
LabelStyle -> labelstyle
]

Comments.
The symbol gridlines
could be instead defined with a DownValues
, as shown by anderstood in his answer. This would read here:
Clear[gridlines];
gridlines[min_, max_] := Table[
If[Divisible[i, 20],
(* main lines *)
{i, Directive[Lighter[Black, 0.5]]},
(* other lines *)
{i, Directive[LightGray, Thin]}
],
{i, Ceiling[min], Floor[max], 2}
];
Update
To get outward ticks, as in the graphics of the question, you can define:
myticks[min_, max_] := Table[
If[Divisible[i, 20],
(* ticks for main lines *)
{i, i, {0, 0.005}},
(* ticks for other lines *)
{i, "", {0, 0.005}}
],
{i, Ceiling[min], Floor[max], 2}
];
frameticks = {{myticks[##] &, None}, {myticks[##] &, None}};
which gives
Graphics[disk,
Frame -> frame, FrameTicks -> frameticks,
PlotRange -> plotrange, GridLines -> gridlines,
LabelStyle -> labelstyle
]

ContourPlot
should only plot a circle, which is the solution of your equation. TryRegionPlot[x^2 + y^2 < 400, {x, -40, 40}, {y, -40, 40}]
instead. Another approach would be usingDisk[]
andLine
. $\endgroup$Disk[]
withgridlines
? $\endgroup$Graphics[{Gray, Disk[{0, 0}, 20]}, Frame -> {{Automatic, None}, {Automatic, None}}, PlotRange -> {{-50, 50}, {-50, 50}}, GridLines -> {Range[-50, 50, 2], Range[-50, 50, 2]}]
. $\endgroup$