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# State whether the following statement is True or False: The line $x+3y=0$ is a diameter of the circle $x^2+y^2+6x+2y=0$.

$\begin{array}{1 1}\text{True}\\\text{False}\end{array}$

• The centre of the circle whose general equation is $x^2+y^2+2gx+2fy+c=0$ is $(-g,-f)$
Equation of the given circle is $x^2+y^2+6x+2y=0$
Hence the centre of the circle is $(-3,-1)$
If the line $x+3y=0$ is the diameter of the circle then
$-3+3(-1)\neq 0$