[" 1.Show that the equations "x^(2)-7x+6=0" and "y^(2)-14y+40=0" form a "],[" parallelogram.Also find the joint equation of its diagonals."]

The lines given by the equation (x^(2)-7x+6)y^(2)-14y+40)=0 form a paralellogram.The combined equation of the line which bisect the angles between their diagonals is:

Show that the equation x ^(2) + y ^(2) + 2x + 10 y + 26 = 0 represents a point circle. Also, find its centre.

The equation to pair of opposite sides of a parallelogram are x^(2)-7x+6=0 and y^(2)-14y+40=0 . The equation of a diagonal is

If pairs of opposite sides of a quadrilateral are x^(2)-7x+6=0 and y^(2)-14y+40=0 then equations of its diagonals are

Show that the equation x^(2)-6xy+5y^(2)+10x-14y+9=0 represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines.

Show that the equation 9x^(2) - 16y^(2) - 18x - 64y - 199 = 0 represents the equation of a hyperbola, find the coordinates of its centre and foci and also the equations of its directrices

A diagonal of the rectangle formed by the lines x^(2)-7x+6=0 and y^(2)-14y+40=0 is