`2x+4y-8xy-1`

Evaluate : 3x^(2) + 5xy - 4y^(2) + x^(2) - 8xy - 5y^(2)

How many integer pairs (x,y) satisfy x^(2) + 4y^(2) -2xy -2x - 4y -8=0 ?

A variable straight line of slope 4 intersects the hyperbola xy=1 at two points. Then the locus of the point which divides the line segment between these two points in the ratio 1:2 , is (A) x^2 + 16y^2 + 10xy+2=0 (B) x^2 + 16y^2 + 2xy-10=0 (C) x^2 + 16y^2 - 8xy + 19 = 0 (D) 16x^2 + y^2 + 10xy-2=0

Add: 4x^(2) - 7xy + 4y^(2) - 3, 5 + 6y^(2) - 8xy + x^(2) and 6 - 2xy + 2x^(2) - 5y^(2)

Show that two pairs of lines 3x^(2)+8xy-3y^(2)=0 and 3x^(2)+8xy-3y^(2)+2x-4y-1=0 forms a square.