" 4."quad " (a) "(x^(2)+y^(2))^(2)=xy

If the foci of a hyperbola lie on y=x and one of the asymptotes is y=2x, then the equation of the hyperbola,given that it passes through (3,4), is (a) x^(2)-y^(2)-(5)/(2)xy+5=0( b) 2x^(2)-2y^(2)+5xy+5=0( c) 2x^(2)+2y^(2)+5xy+10=0 (d)none of these

Determine the degrees of the following polynomials : (x^(4)+x^(2)y^(2)+y^(4))/(x^(2)-xy+y^(2))

Evaluate : (2x-y+3z)(4x^(2)+y^(2)+9z^(2)+2xy+3yz-6xz)

Simplify (4x^(2)y^(2)-9)-:(2xy+3)

Find the following produts: (i) (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2xz)(2x-y+2z)(4x^(2)+y^(2)+9z^(2)+2xy+3yz-6xz)

Find the value of 4x^(2)+y^(2)+25z^(2)+4xy-10yz-20zx when x=4,y=3 and z=2