The curve shown here was actually drawn analytically using the formula
y = a^{3}/(x^{2} + a^{2})
where a is the amplitude, or height, of the curve at the origin (x=0).
Note that to do something 'analytically' means to use a formula.
To create it graphically, start by drawing a circle. Then
pick a point along the x-axis (this point is labeled 'A' in the
animation) and draw a line from the origin ('O'), also seen to be
the bottom of the circle, to point A.
Where this crosses the circle (point 'B') determines the Y value
associated with the X value you first chose. Mark a point horizontally
from point B over at the X value, labeled P(x,y). Do this for a variety
of X-values and you will mark out the curve known as the 'Witch of
Agnesi.' Notice that the curve never quite gets down to a Y value of zero.
This is called asymptotic behavior. It gets ever closer to zero but never
quite reaches it, until X = infinity.