The equation `y^(2)-8y-x+19=0` represents

Show that the equation x^2-2y^2-2x+8y-1=0 represents a hyperbola.

Show that the equation x^2+y^2-6x+8y+21=0 represents a circle.Find the centre and radius of the circle.

The equation x^(3)+x^(2)y+x+y=0 represents

The equation 3x^(2)+10xy-8y^(2) =0 represents

Show that the equation x^(2)-2y^(2)-2x+8y-1=0 represents a hyperbola.Find the coordinates of the centre, lengths of the axes,eccentricity,latusrectum, coordinates of foci and vertices,equations of the directrices of the hyperbola.

The equation x^(2)+y^(2)-6x+8y+25=0 represents

The equation x^(2)+y^(2)-6x+8y+25=0 represents

The equation x^2 - 8x +2y +7 = 0, represents