If `x=4l/(1+l^2) and y = (2-2l^2)/(1+l^2)` where'l' is a parameter and range of `f(x,y) = x^2-xy+y^2` is[a,b] then (a+b) is equal to

if x= 2cos theta ,y= 2sin theta and the range of f(x,y)=x^(2)-xy+y^(2) is [L,M] then the value of the product L.M is equal to

If x = 2 cos θ , y = sin θ and the range of f ( x , y ) = x2 − x y + y2 is [ L , M ] , then the value of the product L.M is equal to

Two tangents to an ellispse x^(2)+2y^(2)=2 are drawn which intersect at right angles,let l_(1) and l_(2) be the intercepts on these tangents made by the circle x^(2)+y^(2)=2 , then l_(1)^(2)+l_(2)^(2) is equal to________

Let L be a tangent line to the parabola y^(2)=4x - 20 at (6, 2). If L is also a tangent to the ellipse (x^(2))/(2)+(y^(2))/(b)=1 , then the value of b is equal to :

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y^(2)=4 respectively, such that the distance d units between L_(1) and L _(2) is minimum, then the value of d is equal to

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y6(2)=4 respectively, such that the distance d units between L_(1) and L _(2) is minimum, then the value of d is equal to

If the circle x^2+y^2+4x+22y+l=0 bisects the circumference of the circle x^2+y^2-2x+8y-m=0 , then l+m is equal to

The vertex of a parabola is the point (a,b) and latusrectum is of length l. If the axis of the parabola is along the positive direction of y-axis, then its equation is : (A) (x+a)^2=l/2(2y-2b) (B) (x-a)^2=l/2(2y-2b) (C) (x+a)^2=l/4(2y-2b) (D) (x+a)^2=l/8(2y-2b)