# Equation Grapher - Implicit Function Grapher

This free online equation grapher is for graphing general equations G(x,y) = F(x,y), where the variables x and y can appear on both sides of the equation. With equation grapher you can also graph implicit functions, standard and general forms of conic sections and level curves.

An equation grapher is a graphing calculator that draws the graph of any equation of the form G(x,y) = F(x,y) where each side is an expression that can contain x and y.

An equation grapher is a more general graphing 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.

An equation graphing calculator can also be used to graph implicitly defined functions.

To graph equations the equal sign must be used to enter both sides of the equation. This allows you to graph, for example, equations of lines in point-slope forms, equations of conic sections (circles, parabolas, hyperbolas and ellipses) and level curves as well as implicit functions.

Tips: As you type:
• pi is replaced by π.
MouseMatics! You can use your mouse to Rotate Axis, Translate and Change Scale

In addition to inputting data — by first pressing the gear button — you can use your mouse to perform some functionality unique to this interactive polar grapher as outlined below.

• Click on (or near) an axis and move your mouse. That will rotate the axis. The graph(s) are re-drawn in the generalized polar coordinate system. Click again to release the axis.
• Drag the mouse to move the coordinate system together with the graphs.
• Double-click in the canvas to move the origin to where was clicked.
• Hold down Alt key and click on an axis to change the scale (zoom in one direction); the point which was clicked will be labelled "1" (or "-1") and becomes the new unit for that axis.
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ResultsHide
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) 🔍+ 1 🔍

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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.

## Instruction

It's easy to use the equation grapher; type in an equation, for example, 3x -2 y = x + 4y in any expression box. The equation grapher 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 displays 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 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: Graph any of the expression under Interesting Graphs clicking on it. For best results you may need to select Graph Fineness as "+1" or higher.

When graphing equations in the form y = f(x) (function) it is recommended to use the function graphing calculator, which draws this type of equations more acurately.

You can set the following options by pressing the ⚙ (gear) button at the top right corner of the graph canvas.

• Change the thickness of the graphs by using the slider provided.