How to draw circles , ellipses , parabolas , squares and all other geometric shapes efficiently without instruments or objects? Often the symmetry of the shapes gets messed up while drawing free-hand. How to overcome this problem?
You haven't said what you're doing the drawing for, but I'm amazed you're even trying to draw these freehand - whenever I do a design drawing, there's no way I can freehand any of that stuff, especially to scale! Circles, straight lines and squares aren't too difficult though - I used to rummage in the kitchen equipment drawer and usually found something the right shape and size to draw round, (pastry cutters, tops off bottles, etc) and for larger circles, might use a saucer or a plate, depending on size. Squares, well anything box shaped of the right size, but parabolas and ellipses, that's another matter altogether - they should be mathematically accurate for one thing. I'm afraid in the end I had to resort to buying the right equipment.
To draw a circle freehand, take a pen/pencil and put your wrist on the piece of paper, then spin/rotate the paper underneath while holding your pen/pencil very firmly. For smaller circles, use your fingers (knuckles) instead of wrist.
Check the videos demonstrating this technique:
For drawing a circle on the larger scale, use your arm by not flexing it.
See the video:
Always try to draw shapes and such things on squared or geometry paper as you can use the squares to keep sides of the shapes the same - you can break it down into quarters and draw one quarter and try and match the others to that one and it should come out pretty neat.