If `x = (4 lambda)/(1+lambda^2)` and `y=(2-2lambda^2)/(1+lambda^2)` where `lambda` is a real parameter and `Z = x^2 + y^2-xy` then possible values of Z can be

If (x+y)^(2)=2(x^(2)+y^(2)) and (xy+lambda)^(2)=4,lambda>0, then lambda is equal to

If lambda_(1),lambda_(2)(lambda_(1)>lambda_(2)) are two values of lambda for which the expression f(x,y)=x^(2)+lambda xy+y^(2)-5x-7y+6 can be resolved as a product of two linear factors, then the value of 3 lambda_(1)+2 lambda_(2) is

Prove that the family of curves x^2/(a^2+lambda)+y^2/(b^2+lambda)=1 , where lambda is a parameter, is self orthogonal.

If the equation x^(2)+y^(2)+2 lambda x+4=0 and x^(2)+y^(2)-4 lambda y+8=0 represent real circles then the valueof lambda can be

If 2(x^(2)+y^(2))+4 lambda x + lambda^(2)=0 represents a circle of meaningful radius, then the range of real values of lambda , is

If 2(x^(2)+y^(2))+4 lambda x + lambda^(2)=0 represents a circle of meaningful radius, then the range of real values of lambda , is

Find all values of lambda for which the (lambda-1)x+(3 lambda+1)y+2 lambda z=0(lambda-1)x+(4 lambda-2)y+(lambda+3)z=02x+(3 lambda+1)y+3(lambda-1)z possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

If the curves C_(1):y=(In x)/(x) and C_(2):y=lambda x^(2) (where lambda is constant) touches each other,then the value of lambda is