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

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

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

The equation, 2x^2+ 3y^2-8x-18y+35= K represents

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

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

In X-Y plane, the path defined by the equation (1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0 , is a parabola if m = (1)/(2), k =- 1, n =0

Find the centre and radius of the circle formed by all thepoints represented by z = x + iy satisfying the relation |(z-alpha)/(z-beta)|= k (k !=1) , where alpha and beta are the constant complex numbers given by alpha = alpha_1 + ialpha_2, beta = beta_1 + ibeta_2 .

If the equation 2x^2+k x y+2y^2=0 represents a pair of real and distinct lines, then find the values of kdot

If (h,k) is a point on the axis of the parabola 2(x-1)^2 + 2(y-1)^2 = (x+y+2)^2 from where three distinct normal can be drawn, then the least integral value of h is :