Question

Useful to plot points on Socratic Graph?

Answer 1

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]}

Answer 2

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]}