Graph of implicit function f(x,y) = 0
Input only f(x,y) and g(x,y) (g is not mandatory), do not input " = 0 ".
How to use this calculator ?
• f(x,y) : two variables function that defines the graph to plot.
The graph connects points (x,y) of the plane that verifie f(x,y) = 0 (do not input the second equality member " = 0 ").
Note that the two variables of f are always x and y.
• g(x,y) : second optional graph to plot.
• xmin and xmax : Mandatory fields. This is the range of x-coordinates to include in the plot.
• ymin and ymax : Mandatory fields. This is the range of y-coordinates to include in the plot.
You may input numbers, fractions, operators and common functions.
- Operators : + - * / and ^ (power)
- Constants : pi, e
- Common functions : sqrt (= square root), log, exp, etc
- Trigonometric functions : cos, sin, tan, cot, arccos, arcsin, arctan, arccot, etc
Authorized functions are listed in this calculator : authorized functions
• Example 1. Draw an ellipse given its equation : `(x-2)^2/5+(y-7)^2/15=7`
In this case the ellipse is defined by the implicit function `f(x,y)=(x-2)^2/5+(y-7)^2/15-7=0`
Then input f(x,y) in the form above to get the following ellipse graph.
• Example 2. Visually check the intersection between a conic section of equation `x+5xy+8y=7` and the line of equation `y =x-1`
The conic section is defined by the implicit function `f(x,y)=x+5x*y+8y-7=0`
The line is defined by the implicit function `g(x,y)=y-x+1=0`
So, we input f(x,y) and g(x,y) in the calculator above to get following graph.