The equation `ax^2+y^2+bxy-74x-78y+212=0` represents

The equation 16x^(2)+y^(2)+8xy-74x-78y+212=0 represents

The equation 16x^(2)+y^(2)+8xy-74x-78y+212=0 represents

The equation x^(2) + y^(2) - 2xy -1 =0 represents :

The second degree equation x^(2)+4y^(2)-2x-4y+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 3ax^2+9xy+(a^2-2)y^2=0 represents two perpendicular straight lines for