Show that pair of straight lines $ax^{2}+2hxy+ay^{2}+2gx+2fy+c=0$ meet coordinate axes in concyclic points. Also find equation of the circle Show that pair of straight lines $ax^{2}+2hxy+ay^{2}+2gx+2fy+c=0$ meet coordinate axes in concyclic points. Also find equation of the circle through those cyclic points
My Attempt:
Given equation to the pair of straight lines is
$ax^2+2hxy+ay^2+2gx+2fy+c=0$
Let the lines be
$l_1x+m_1y+n_1=0$
and 
$l_2x+m_2y+n_2=0$
Now what should I do next?

Begin by finding intercepts:
$$ax^2+2hxy+ay^2+2gx+2fy+c=0$$
For x intercepts,
$$ ay^2 + 2fy +c = 0$$
For y intercepts,
$$ ax^2 + 2gx + c = 0$$
Let the points corresponding to root be: $(a,0) , (b,0) , (0,c) , (0,d)$
From this answer here, the equation of circle through these points:
$$
   \det\begin{bmatrix}
     x^2 +y^2 & x & y & 1 \\
     b^2 & b & 0 & 1 \\
     c^2 & 0 & c& 1 \\
    d^2 & 0 & d& 1 \\
   \end{bmatrix} = 0
$$
For checking if $(a,0)$ is on this circle , simply plug it in place of $(x,y)$
