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`|`< k `, then the value of 4k is______

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 auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

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

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 .

From any point P lying in the first quadrant on the ellipse (x^2)/(25)+(y^2)/(16)=1,P N is drawn perpendicular to the major axis and produced at Q so that N Q equals to P S , where S is a focus. Then the locus of Q is (a) 5y-3x-25=0 (b) 3x+5y+25=0 (c) 3x-5y-25=0 (d) none of these

If from a point P , tangents P Qa n dP R are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

Find the locus of point P such that the tangents drawn from it to the given ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meet the coordinate axes at concyclic points.

If the midpoint of the chord of the ellipse x^2/16+y^2/25=1 is (0,3)

The eccentricity of the ellipse 16x^2 + 25y^2 = 400 is

Find the equation of a chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 joining two points P(pi/4) and Q((5pi)/4)