If point P(x, y) is such that it moves on a hyperbola `|sqrt((x-3)^2 +(y-4)^2)-sqrt(x^2+y^2)|=k^2` then number of possible integral values of k is

If the line 3x+4y=k is tangent to the circle x^2+y^2-2x-4y+4=0 , then number of integral values of k is

If the line 3x+4y=k is tangent to the circle x^2+y^2-2x-4y+4=0 , then number of integral values of k is

The equation |sqrt(x^(2)+(y-1)^(2))-sqrt(x^(2) +(y+1)^(2))| = k will represent a hyperbola for-

The locus of a point P(x, y) satisfying the equation sqrt((x -2)^(2) + y^(2)) + sqrt( (x + 2)^(2) + y^(2)) = 4 , is

If sqrt(a^(2)-x^(2))+sqrt(a^(2)-y^(2))=k(x-y) then (dy)/(dx)=

If the equation |sqrt((x - 1)^(2) + y^(2) ) - sqrt((x + 1)^(2) + y^(2))| = k represents a hyperbola , then k belongs to the set

If the equation |sqrt((x - 1)^(2) + y^(2) ) - sqrt((x + 1)^(2) + y^(2))| = k represents a hyperbola , then k belongs to the set

If x sqrt(1-y^(2))+y sqrt(1-x^(2))=k , then the value of (dy)/(dx) at x=0 is -

If the locus of the moving point P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.