# Useful to plot points on Socratic Graph?

Jul 31, 2015

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 $\left(y - {x}^{2}\right) = 0$. then you can add more curves if you can express them in the form $f \left(x , y\right) = 0$. Let me have a go at adding some small circles to $y = {x}^{2}$ by graphing:

$\left(y - {x}^{2}\right) \left({x}^{2} + {y}^{2} - 0.04\right) \left({\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} - 0.04\right) \left({\left(x + 2\right)}^{2} + {\left(y - 4\right)}^{2} - 0.04\right) = 0$

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

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

#### Explanation:

To show the point $\left(2 , 3\right)$
Graph ${\left(x - 2\right)}^{2} + {\left(y - 3\right)}^{2} = \frac{1}{100}$
(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:

${\left(x - 2\right)}^{2} + {\left(y - 3\right)}^{2} \le \frac{1}{100}$

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

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

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} - {r}^{2} = 0$ and multiply:

$\left(2 , 3\right)$ and $\left(4 , - 2\right)$

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 $y = 2 x + 4$

Using

$\left(y - {x}^{2}\right) \left(y - 2 x - 4\right) = 0$

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