# Equation Grapher Online | Implicit Function Grapher

Explor our equation grapher, a sophisticated grapher that can graph general equations in rectangular and oblique Cartesian coordinate systems, including implicitly defined functions.

An equation grapher is a more versatile tool than a function grapher, which only draws the graph of equations in the form `y = f(x)` where the right hand side is an expression in `x` only.

To graph an equation `f(x,y) = g(x,y)`, the equal sign must be used to enter both sides of the equation. This allows you to graph, for example, the equation of a line in the point-slope form, equation of a conic sections (circles, parabolas, hyperbolas and ellipses) and level curves as well as implicit functions.

Our online equation grapher uses a sophisticated algorithm that we developed to graph equations of the form `f(x,y) = g(x,y)`.

Using this algorithm, the process of equation graphing starts by investigating rows of pixels on the canvas to find the zeros of `f(x,y)-g(x,y)` for each value of `y`, applying Newton's method.

Our equation grapher then uses implicit differentiation to draw tiny tangent lines at those points `(x,y)` that satisfy the equation. This way, the graph is drawn.

The quality of the resulting graph is controlled by the Graph Fineness setting, which allows users to choose how accurate the graph should be. The higher the Graph Fineness setting, the more accurate the graph will be, but it will also take longer to graph the equation.

As you type:
• pi is replaced by π.
x y
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Equations

Lines

y = 1 x = 1 y = x+1 x = y+1 3x + y = 2 3x - y +5 = 4x+2y-2

Circles

x^2+y^2 = 9 (x-2)^2 + (y-2)^2 = 4

Ellipses

x^2/4 + y^2/9 = 1 x^2-xy+2y^2-x-2y-8=0

Parabolas

y=x^2 y = x^2-4x+4 2x^2-4xy+2y^2-x-2y-2=0

Hyperbolas

x^2/4 - y^2/9 = 1 24x^2-50xy-49y^2+97x+93y-164=0

Other graphs

x^2 = y^2 sin(xy) = cos(xy)
Equations — Polar
Currently, not available.
RAD
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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the pop-up menu.

MouseMatics: Learn how you can use your mouse to rotate axes, change scales, and move coordinate system.

## Instructions

It's easy to use the equation grapher; type in an equation, for example, 3xy - 2y = x^2 + 4y in any expression box. The equation grapher plots the graphs as you type (default).

• To graph two or more equations on the same coordinate system press » to display the multi-graph pane. The multi-graph pane consists of expression panels, which can be added or deleted as desired by pressing + or × on each panel, respectively. Selecting or deselecting the checkbox for any expression shows or hides the corresponding graph.
• You can set the fineness of the graphs by selecting the desired option from Graph Fineness drop-down list. In general, the higher the accuracy, the longer it takes the equation grapher to graph equations.
• To copy or save the graphs first press the Copy/Save graph button. An image of the graphs will appear below the equation grapher. You can then use your browser's capability to save it or copy it in your documents.

Interesting curves: Click on any of the equations under Interesting Graphs to graph it. For best results you may need to select a higher Graph Fineness setting.

Click the ⚙ (gear) button at the top right corner of the graph canvas to set the following options.

• Use the slider to change the thickness of the graphs.
• Select the angle mode (radiansdefault, degrees or grades).
• If you deselect the Graph as you type option, you will need to press Graph selected expressions at the bottom of the calculator to update the graphs whenever you make any changes to the equations or coordinate plane (such as moving the origin or rotating the axes).
• Optionally display the controls on the top of the equations grapher that enable you to start/pause and stop rotation of any or all axes.
• The equations grapher remembers the equations expressions you enter and retrieves them between visits. You can clear them by pressing the Reset Calculator button.

### Graphing Equations in Oblique Coordinate Systems

Our equation grapher is the only one that enables you to rotate axes. This allows you to graph equations in an oblique coordinate system, where any axis can be at any angle from the horizontal and have any orientation.