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` , such that `|alpha|

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)

Two perpendicular tangents drawn to the ellipse (x^(2))/(25)+(y^(2))/(16)=1 intersect on the curve.

The mid point of the chord 16x+9y=25 to the ellipse (x^(2))/(9)+(y^(2))/(16)=1 is

From a point (2,alpha) tangents are drawn to the same branch of hyperbola (x^(2))/25-(y^(2))/16=1 , then the range of alpha epsilon(l_(1),l_(2)) then l_(2) is equal to_________

Angle between the tangents drawn from point (4, 5) to the ellipse x^2/16 +y^2/25 =1 is

If two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

Number of normals that can be drawn through the point (0,(1)/(2)) to the ellipse (x^(2))/(2)+(y^(2))/(1)=1 is ______

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is