`x=at^(2),y=2at`,

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)

Form the differential equation of the family of curves represented by the equation (a being the parameter): (2x+a)^(2)+y^(2)=a^(2)(2x-a)^(2)-y^(2)=a^(2)(x-a)^(2)+2y^(2)=a^(2)

If x^(2)+(x)/(y^(2))=y^(2)+(y)/(x^(2))=2 then find x^(2)+y^(2)

Add : x^(2) y^(2) , 2x^(2)y^(2) , - 4x^(2)y^(2) , 6x^(2)y^(2)

If x/y = (a + 2)/(a - 2) , then show that (x^(2) - y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4) .

Find the area of the region {(x,y):x^(2)+y^(2) =2}

The locus of a point,from where the tangents to the rectangular hyperbola x^(2)-y^(2)=a^(2) contain an angle of 45^(0), is (x^(2)+y^(2))^(2)+a^(2)(x^(2)-y^(2))=4a^(2)2(x^(2)+y^(2))^(2)+4a^(2)(x^(2)-y^(2))=4a^(2)(x^(2)+y^(2))^(2)+4a^(2)(x^(2)-y^(2))=4a^(2)(x^(2)+y^(2))+a^(2(x^(2)-y^(2)))=a^(4)

If a=(x)/(x^(2)+y^(2))and b=(y)/(x^(2)+y^(2)). The value of (x+y) is