Check Whether The line x+3y=0 is a diameter of the circle `x^(2)+y^(2)+6x+2y=0`

Explanation

To determine whether the line \( x + 3y = 0 \) is a diameter of the circle given by the equation \( x^2 + y^2 + 6x + 2y = 0 \), we can follow these steps:

### Step 1: Rewrite the Circle Equation in Standard Form
The standard form of a circle's equation is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
...