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

Find the locus of image of the variable point (lambda^(2), 2 lambda) in the line mirror x-y+1=0, where lambda is a parameter.

If the locus of the image of the point (lambda^(2), 2lambda) in the line mirror x-y+1=0 (where lambda is a parameter) is (x-a)^(2)=b(y-c) where a, b , c in I , then the value of ((a+b)/(c+b)) is equal to

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

Tangents are drawn from a point P to the hyperbola x^2/2-y^2= 1 If the chord of contact is a normal chord, then locus of P is the curve 8/x^2 - 1/y^2 = lambda where lambda in N .Find lambda

Tangents are drawn from a point P to the hyperbola x^2/2-y^2= 1 If the chord of contact is a normal chord, then locus of P is the curve 8/x^2 - 1/y^2 = lambda where lambda in N .Find lambda

Find the locus of image of the veriable point (lambda^(2), 2 lambda) in the line mirror x-y+1=0, where lambda is a peremeter.

Find the locus of image of the veriable point (lambda^(2), 2 lambda) in the line mirror x-y+1=0, where lambda is a peremeter.

Find the locus of image of the veriable point (lambda^(2), 2 lambda) in the line mirror x-y+1=0, where lambda is a perimeter.