If locus of point from where two of three normal to curve `y^(2)+2y-4x+5=0` are perpendicular is `(y-(k)/(2))^(2)-(x-lambda)=0` ,then value of `(lambda-2k)` 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 (x+y)^(2)=2(x^(2)+y^(2)) and (xy+lambda)^(2)=4,lambda>0, then lambda is equal to

If the locus of the middle points of the chords of the parabola y^(2)=2x which touches the circle x^(2)+y^(2)-2x-4=0 is given by (y^(2)+1-x)^(2)=lambda(1+y^(2)), then the value of lambda is equal to

The area between the curves x=4y-y^(2) and 0 is lambda square units, then the value of 3lambda is equal to

If 2x-3y=0 is the equation of the common chord of the circles x^(2)+y^(2)+4x=0 and x^(2)+y^(2)+2 lambda y=0 then the value of lambda is

The lines joining the point of intersection of the line x+y=1 and the curve x^2+y^2-2y+lambda=0 to the origin are perpendicular, then value of lambda wil be: (A). 1/2 (B). -1/2 (C). 1/sqrt2 (D). 0

Tangents are drawn to the curve y=sin x from the origin.Then the point of contact lies on the curve (1)/(y^(2))-(1)/(x^(2))=lambda. The value of lambda is equal to

If three normals are drawn from the point (c, 0) to the parabola y^(2)=4x and two of which are perpendicular, then the value of c is equal to

If 3x+4y-k is the equation of the normal to the curve x^(2)+2x-3y+3=0 at the point (1,2) ,then the value of k=