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 fromn 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

IF alpha , beta are eccentric angles of end points of a focal chord of the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 then tan(alpha /2) tan (beta/2) is equal to

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 (a sec alpha,b tan alpha) and (a sec beta ,b tan beta) be the ends of a chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passing through the focus (ae,0) then tan (alpha/2) tan (beta/2) is equal to

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1 subtends a right angle at the vertex A(a,0), then prove that tan((a)/(2))tan((beta)/(2))=-(b^(2))/(a^(2))

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

If alpha and beta be the angles subtended by the major axis to an ellipse at the extremities of a pair of conjugate diameters then cot^(2)alpha+cot^(2)beta is equal to

If alpha,beta are the eccentric angles of the extremities of a focal chord of the ellipse x^(2)/16 + y^(2)/9 = 1 , then tan (alpha/2) tan(beta/2) =