Correct Answer - 1,2,3,4
The given circle is `x^(2)+y^(2)+2hxy+2gx+2fy+c=0` (i)
For (i) to represent a circle, `h=0`
So, the given circle is
`x^(2)+y^(2)+2gx+2fy+c=0` (ii)
For circle (ii) to pass through the quadrants only.
I. Circle must cut x-axis `i.e., g^(2)-c gt0`
II. Circle must cut y-axis `g^(2)-cgt0`
III. The origin should lie outside circle `(ii) , i.e., cgt0`
Therefore, the required conditions are `g^(2) gt c, f^(2) gt c, cgt 0` and `h=0`.