The equation `|sqrt(x^2+(y-1)^2)-sqrt(x^2+(y+1)^2)|=K` will represent a hyperbola for (a)`K in (0,2)` (b) `K in (-2,1)` (c)`K in (1,oo)` (d) `K in (0,oo)`

The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents a parabola for k (1^2+m^2)^(-1) a point circle for k=0

The equation (x^2)/(12 - k) + (y^2)/(8 - k) = 1 represents a hyperbola whose transverse axis is along the x axis if

Equation x^(2) +k_(1)y^(2) +2k_(2)y = a^(2) represents a pair of perpendicular straight lines if

If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k =

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [(1,1)/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [(1,1)/k] (d) alpha+beta=0 for x in [-k , k]

The equation 3x^2+4y^2-18x+16 y+43=k (a)represents an empty set, if k 0 (c)represents a point, if k=0 (d)cannot represent a real pair of straight lines for any value of k

If the inequality cot^(2)x + (k +1) cot x - (k-3) < 0 is true for at least one x in (0, pi//2) , then k in .

If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then the value of k for which S+K=0 represents its asymptotes is 20 (b) -16 (c) -22 (d) 18

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2