# How to find the equation of diameter of a circle that passes through the origin?

So this was a question that I was solving that got me stuck. Its as follows: Q. Find equation of diameter of the circle $x^2 + y^2 - 6x + 2y = 0$ which passes through the origin.

Now I have tried the following,

From the equation I found, $g=(-3)$ and $f=1$ and subsequently found the radius as $r=\sqrt{10}$ and hence diameter as $d=2\sqrt{10}$.

But I cant seem to understand how to progress, help would be greatly appreciated.

Hint: Complete the squares in $x$ and $y$.
You know the centre of the circle and you have the point $(0,0)$ (which lies on the circle). Those are two points in $\mathbb R^2$. Now just calculate the distance between those two points.