Find the eccentric angles of the extremities of the latus recta of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`

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

Find the eccentricity and the length of the latus rectum of the ellipse (x^(2))/(4) + (y^(2))/(25) = 1 .

Find the area of the region bounded by the latus recta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the targets to the ellipse drawn at their ends

Find the eccentricity and the length of the latus rectum of the ellipse (x^(2))/(49) + (y^(2))/(36) = 1 .

Find the area of parallelogram formed by tangents at the extremities of latera recta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The locus of extremities of the latus rectum of the family of ellipse b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2) is