# Is it possible to plot a second-order curve by its non-canonical equation? [closed]

I have this second-order polynom:

$$6xy+8y^2-12x-26y+11=0$$

And I need to reduce it to a canonical form of a second-order curve. I solved this, but is it possible to draw a plot of the original equation to check whether my solution is correct? Something like

Plot[6 x*y + 8 y^2 - 12 x - 26 y + 11, {x, -20, 20}, PlotRange -> {-20, 20}]


Now this draws an empty plot.

Thank you.

• Look up ContourPlot. Also, you need a space between x and y, otherwise it denotes a different variable named xy.
– user484
Commented Jul 29, 2014 at 8:13
• @RahulNarain thank you for spotting xy.
– d.k
Commented Jul 29, 2014 at 8:15

As @Rahul said in a comment (beat me to it!), have a look at ContourPlot:

ContourPlot[
6 x y + 8 y^2 - 12 x - 26 y + 11 == 0,
{x, -20, 20},
{y, -20, 20}
]


• could you suggest how can I draw the x and y axes on this plot, please?
– d.k
Commented Jul 29, 2014 at 8:23
• @user5693 Then you can give the option FrameLabel: ContourPlot[...., FrameLabel -> Automatic]. This is actually given in the documentation (admittedly buried a bit, but still). Commented Jul 29, 2014 at 8:31
• sorry, my question was incorrect to some point. I meant to set axes origin at 0,0, is it possible? Google says nothing
– d.k
Commented Jul 29, 2014 at 8:32
• @user5693 Ah sorry I misunderstood; that's ContourPlot[..., Axes -> True, Frame -> False]. (Can also be found in the documentation of ContourPlot!). Commented Jul 29, 2014 at 8:36