Useful to plot points on Socratic Graph?

2 Answers
Jul 31, 2015

Answer:

You may be able to add small circles to a graph using their equations.

Explanation:

Firstly, instead of requesting (say) a graph of #x^2#, request a graph of #(y-x^2) = 0#. then you can add more curves if you can express them in the form #f(x, y) = 0#. Let me have a go at adding some small circles to #y = x^2# by graphing:

#(y-x^2)(x^2+y^2-0.04)((x-2)^2+(y-4)^2-0.04)((x+2)^2+(y-4)^2-0.04) = 0#

graph{(y-x^2)(x^2+y^2-0.04)((x-2)^2+(y-4)^2-0.04)((x+2)^2+(y-4)^2-0.04) = 0 [-5.165, 4.835, -0.46, 4.54]}

Aug 12, 2015

Answer:

Graph a circle of small radius, centered at the point of interest.

Explanation:

To show the point #(2,3)#
Graph #(x-2)^2+(y-3)^2 = 1/100#
(Use some other radius if you prefer.)

graph{(x-2)^2+(y-3)^2 = 1/100 [-10, 10, -5, 5]}

For a single point, you can even fill in the circle by using an inequality:

#(x-2)^2+(y-3)^2 <= 1/100#

graph{(x-2)^2+(y-3)^2 <= 1/100 [-10, 10, -5, 5]}

To plot two or more points, use circles in the form:

#(x-h)^2+(y-k)^2-r^2 = 0# and multiply:

#(2,3)# and #(4,-2)#

graph{((x-2)^2+(y-3)^2 - 1/100)((x-4)^2+(y+2)^2 - 1/100)=0 [-1.904, 15.874, -3.68, 5.21]}

The problem with this method is that it is very sensitive to zoom and centering. At some zooms/centers one or both circles will disappear.

Of course, you can use the same two equation idea to graph two curves:

Graph:

#y = x^2# and #y = 2x+4#

Using

#(y-x^2)(y-2x-4) = 0#

graph{(y-x^2) (y-2x-4)= 0 [-11.25, 20.78, -3.48, 12.54]}