If the equation x2+y2+2hxy+2gx+2fy+c=0 represents a circle, then the condition for that circle to pass through three quadrants only but not passing through the origin is

The given circle is x2+y2+2hxy+2gx+2fy+c=0 -----(i) For (i) to represent a circle , h = 0. So, the given circle is x2+y2+2gx+2fy+c=0 ------(ii) For circle (ii) to pass through three quadrants only,I. Circle must cut x-axis. i.e., g2−c>0.II. Circle must cut y-axis. g2 - c> 0.III. The origin should lie outside circle (ii), i.e., c > 0.Therefore, the required conditions are g2>c,f2>c,c>0 and h = 0.