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

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a circle of non-zero radius , if

If the equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a circle with X-axis as a diameter , and radius a, then :

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

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

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

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of straight line,show that their point of intersection is (sqrt((f^(2)-bc)/(h^(2)-ab)),sqrt((g^(2)-ac)/(h^(2)-ab)))

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of straight line,show that they intersect in point ((hf-bg)/(ab-h^(2)),(hg-af)/(ab-h^(2)))