If the lines 2x + 3y + 1 = 0, 6x + 4y + 1 = 0 intersect the co-ordinate axes in 4 points, then the circle passing through the points is

When a circle passing through the 4 points where the lines intersecting on the axes, the points are called concyclic points. Then the equation of the circle is  ${\text{L}}_1{L}_2 -xy term$ 

Given lines are $2x+3y+1=0,\mathrm{........}\left(1\right)$   $6x+4y+1=\mathrm{0........}\left(2\right)$ 

The equation of the circle is $\left(1\right)\left(2\right)-xyterm=0$

$\left(2x+3y+1\right)\left(6x+4y+1\right)-26xy=0$

$\Rightarrow 12x^2+12y^2+8x+7y+1=0$