The value of a for which `(13x-1)^(2)+(13y-2)^(2)=(a^(2)-1)(5x+12y-1)^(2)` repesents an ellipse is

The set of values of a for which (13x-1)^(2)+(13y-2)^(2)=a(5x+12y-1)^(2) represents an ellipse is

The set of values of 'a' for which (13 x-1 ) ^(2) + (13y -2) ^(2) =a( 5x+ 12y -1)^(2) represents an ellipse if

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)

The equation (13x -1)^(2) + (13y -1)^(2) =k (5x-12y+1)^(2) will represent a parabola, if

The equation (13x -1)^(2) + (13y -1)^(2) =k (5x-12y+1)^(2) will represent a parabola, if

If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)+(y-3)^(2)}=(5x-12y+17)^(2) is L then the value of 13L/4 is _________.

If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)+(y-3)^(2)}=(5x-12y+17)^(2) is L then the value of 13L/4 is _________.

If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)+(y-3)^(2)}=(5x-12y+17)^(2) is L then the value of 13L/4 is _________.

If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)+(y-3)^(2)}=(5x-12y+17)^(2) is L then the value of 13L/4 is _________.