Which Geometry Shape Is $3x^2+3y^2-10y+3=0$

Question

$3x^2+3y^2-10y+3=0$

Wolfram says it is a circle, I know a circle is of the form $(x-a)^2+(y-b)^2=r^2$

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Answer 1

Wolfram is right (of course).

Note that you can write it as (divide by three and write them as squares):

$$x^2+(y-\tfrac{5}{3})^2-\tfrac{25}{9}+1=0$$

and so it's equivalent to

$$x^2+(y-\tfrac{5}{3})^2=(\tfrac{4}{3})^2$$

So yeah. It's a circle.

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Sidenote; I see that you say a circle is of the form $(x-a)^2+(y-b)^2=0$; this is not true. A circle is of the form $(x-a)^2+(y-b)^2=c^2$.