If the normals at the points P Q, R with eccentric angles `alpha, beta, gamma` on the ellipse `x^2/a^2 + y^2 / b^2 = 1` lare concurrent, then show that

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

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 =

The eccentric angles of the ends of L.R. of the ellipse (x^(2)/(a^(2))) + (y^(2)/(b^(2))) = 1 is

The eccentric angles of the ends of L.R. of the ellipse (x^(2)/(a^(2))) + (y^(2)/(b^(2))) = 1 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 .

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 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 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

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