The condition that the lines `ax+hy+g=0, hx+by+f=0, gx+fy+c=0` to be con-current is

Find the condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 to take the form aX^(2) + 2hXY + bY^(2) = 0 when the axes are translated.

The condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy +c=0 can take the form ax^(2) - 2hxy + by^(2)=0 , when shifting the origi is

The condition that the line (x + g) cos theta + ( y +f ) sin theta = k is a tangent to x^2+y^2 +2gx +2fy +c=0 :

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then