I was trying to graph Lituus using polar equation $r^2 \theta=a$
Here $a$ is a constant.
But when I try to convert it into Cartesian equation the graph looks bizarre.
$$y=x \tan(\frac{a}{(x^2+y^2}))$$
.
Can anyone explain this, why is it happening?
Here is pictures
.
.
2026-03-29 16:27:02.1774801622
Problem with graphing equation in polar form vs Cartesian form
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The function $$\tan (\frac {a}{x^2+y^2})$$ is undefined for points where $$ \frac {a}{x^2+y^2}= (2k+1)\pi /2$$
Which makes your graph missing some points.
Note that the two equations are not exactly the same because of asymptotic behavior of the tangent function.