There is no standard instrument for drawing parabolas, as a compass for circles. Although one can cut a parabola from cardboard, in which case they will need some openings in the template to see where the axis is located.

The equation of the circle is `x^2 + y^2 = R^2 , ` while the equations of the axes are `x = 0 , ` `y = +- sqrt ( 3 ) x , ` and `y = +- 1 / sqrt ( 3 ) x .`

The first parabola has the equation `y = R + x^2 / 16 . ` It is simple to reflect it over the x-axis to get `-y = R + x^2 / 16 , ` but to get other equations we need to perform at least one rotation, say by `pi / 3 .`

The formulas are `x = 1/2 x' - sqrt(3)/2 y' , ` `y = sqrt(3)/2 x' + 1/2 y' , ` so the equation of a rotated parabola is

`sqrt(3)/2 x' + 1/2 y' = R + 1/16 (1/2 x' - sqrt(3)/2 y')^2`

The other three parabolas can be obtained from this equation by changing x to -x, y to -y, and both.

A platform that can draw such equations can be seen in the link attached.

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**Further Reading**