The circle ax2 + ay2 + 2gx + 2fy + c = 0 meets x-axis at two points on opposite sides of the origin. What`s the condition?(1)a>0 (2)c0

To find intersection of circle with x-axis put y=0, hence we get

ax² + 2gx + c = 0

now this quadratic eqn must have real roots and both root lies on opposite side of origin

hence a> 0 and c<0 or a<0 and c>0