Let the eccentric angles of three points `P,Q and R` on the ellipse `x^2/a^2+y^2/b^2= 1` be `alpha,pi/2+alpha and pi+alpha` an A circle through `P, Q and R` cuts the llipse again at S, then the eccentric angle of S is

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 eccentric angles of the any two points P,Q on the ellipse x^2/a^2+y^2/b^2=1 are (alpha+beta) and (alpha-beta) resp.Show that the equation of chord PQ is x/a cosalpha+y/b sinalpha=cosbeta

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

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)

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

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 .

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

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

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 =