If a chord joining two points whose eccentric angles are `alpha and beta` so that `tan alpha . tan beta=-a^2/b^2` , subtend an angle `theta` at the centre of the ellipse `x^2/a^2+y^2/b^2=1` then `theta=`

If the chord joining two points whose eccentric angles are alpha and beta cut the major axis of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distance from the centre then tan (alpha)/(2).tan (beta)/(2) =

If the chord, joining two points whose eccentric angles are alpha and beta , cuts the major axis ofthe ellipse x^2/a^2 + y^2/b^2=1 at a distance c from the centre, then tan alpha//2.tan beta//2 is equal to

If the chord, joining two points whose eccentric angles are alpha and beta , cuts the major axis ofthe ellipse x^2/a^2 + y^2/b^2=1 at a distance c from the centre, then tan alpha//2.tan beta//2 is equal to

If the chord,joining two points whose eccentric angles are alpha and beta, cuts the major axis ofthe ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distance crromn the centre,then tan alpha/2.tan beta/2 is equal to

If (alpha-beta)=(pi)/(2) ,then the chord joining the points whose eccentric angles are alpha and beta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(k) , then ( 5k^(2)+2) is equal to