To remove the first degree terms from the equation `ax^(2)+by^(2)+2gx+2fy+c=0`where `a!=0,b!=0` the origin shifted to the point

In order to eliminate the first degree terms in the equation 2x^(2)-2y^(2)+z^(2)-4x+8y+2z-5=0 the origin should be shifted to the point

To remove the first degree terms of the equation 2xy+4x-2y+7=0 the shifted origin is

To remvoe the first dgree terms in the equation 4x^(2)+9y^(2)-8x+36y+4=0 , the origin in shifted to the point

In order to eliminate the first degree terms from the equation 2x^(2)-4xy+5y^(2)-4x-2y+7=0 then point to which origin is to be shifted is

ax^2+2hxy+by^2+2gx+2fy+c=0

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a circle if

If the equation ax^(2)+ay^(2)+2gx+2fy+c=0 represents a pair of lines then

If the lines represented by the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 are equidistant from the origin, then

For the equation ax^(2) +by^(2) + 2hxy + 2gx + 2fy + c =0 where a ne 0 , to represent a circle, the condition will be