`alpha and beta` are eccentric angles of two points A and B on the ellipse `x^2/a^2+y^2/b^2=1` If P `(a cos theta , b sin theta)` be any point on the same ellipse such that the area of triangle PAB is maximum then prove that `theta=(alpha+beta)/2`

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is

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 (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .

If the eccentric angles of the two points on the ellipse (x^(2))/(a^(2)) =(y^(2))/(b^(2)) = 1 (a^(2)gt b^(2)) and theta_(1) and theta_(2) then prove that the equation of chord passing through these two point is (x)/(a)"cos"(theta_(1)+theta_(2))/(2)+(y)/(b)"sin"(theta_(1)+theta_(2))/(2)="cos" (theta_(1)-theta_(2))/(2) .

The area of the triangle formed by three points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentric angles are alpha,beta and gamma is

Area of the triangle formed by the tangents at the point on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha,beta,gamma is

The points P Q R with eccentric angles theta, theta+alpha, theta+2 alpha are taken on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then if area of triangle PQR is maximum then alpha =