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

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

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)

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 y=(tan^(-1)x)^(2), then prove that (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)=2

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)

The equation sqrt((x-2)^(2)+y^(2))+sqrt((x+2)^(2)+y^(2))=4 represents