If `theta_1,theta_2` are the eccentric angles of the extremities of a focal chord of the ellipse `x^2/a^2+y^2/b^2=1(a lt b) and e` is the eccentricity then show that `(e+1)/(e-1)=cot((theta_1)/2)cot((theta_2)/2)`

If theta_(1),theta_(2) are the eccentric angles of the extremities of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a

If 0_1 0_2 are the eccentric angles of the extremeties of a focal chord (other that the verticles) of the ellipse x^2/a^2+y^2/b^2=1 (agtb and e its its eccentricity. Then show that (e+1)/(e-1)=cot(0_1/2).cot(0_2/2) .

If 0_1 0_2 are the eccentric angles of the extremeties of a focal chord (other that the verticles) of the ellipse x^2/a^2+y^2/b^2=1 (agtb) and e its its eccentricity. Then show that e cos ""((0_1+0_2))/2=cos""((0_1-0_2))/2

IF alpha,beta are the eccentric angles of the extremities of a focal chord of the ellipse x^2/a^2+y^2/b^2=1 . Then show that e cos""(alpha+beta)/2=cos""(alpha-beta)/2

If the eccentric angles of the ends of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb) are theta_(1) and theta_(2) , then value of "tan"(theta_(1))/(2) "tan"(theta_(2))/(2) equals

Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentricity e is

If theta and phi are eccentric angles of the ends of a pair of conjugate diametres of the ellipse x^2/a^2 + y^2/b^2 = 1 , then (theta - phi) is equal to