Find the range of values of `lamda` for which the point `(lamda,-1)` is exterior to both the parabolas `y^(2)=|x|`.

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

Find the range of y= x/(1 + x^2)

Find the focus of the parabola y=x^2+x+1 .

The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda =

Find the value of lamda for which the inequality 3-abs(x-lamda)gtx^2 is satisfied by atleast one negative x in R.

Find the focus of the parabola y = x^(2) + x + 1 .

The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=0 . The third side, which is variable, always passes through the point (-5,-1) . Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.

Find the range of values of m for which the line y=m x+2 cuts the circle x^2+y^2=1 at distinct or coincident points.

Find the point where the line x+y=6 is a normal to the parabola y^2=8x .

Find the area of that part of the circle "x"^2+" y"^2=16 which is exterior to the parabola "y"^2=6"x"dot