[" If "x=(4 lambda)/(1+lambda^(2))" and "y=(2-2 lambda^(2))/(1+lambda^(2))],[" where "lambda" is a real parameter,then "x^(2)-xy+y^(2)],[" lies in the interval "[a,b]," then "(a+b)" is: "]

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

The locus of the point x=a+lambda^(2),y=b-lambda where lambda is a parameter is

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

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

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C, where A, B and C are matrices then A+B=

If sin2x cos2x cos4x=lambda has a solution then lambda lies in the interval

Prove that the tangents to family of hyperbola (x^(2))/(b^(2)+lambda)-(y^(2))/(b^(2))=1 (where lambda is a real parameter) at their point of intersection with x^(2)-y^(2)=2b^(2)+lambda^(2) are a pair of fixed lines. Find the equations of the lines.

If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R , then lambda belongs to the interval :

If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R , then lambda belongs to the interval :