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` =

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

The area of the parallelogram formed by the tangents at the points whose eccentric angles are theta, theta +(pi)/(2), theta +pi, theta +(3pi)/(2) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

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 P and Q are points with eccentric angles theta and (theta+(pi)/(6)) on the ellipse (x^(2))/(16)+(y^(2))/(4)=1 , then the area (in sq. units) of the triangle OPQ (where O is the origin) is equal to

If P(theta),Q(theta+(pi)/(2)) are two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and a is the angle between normals at P and Q, then

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 a chord joining two points whose eccentric angles are alpha and beta so that tan alpha.tan beta=-(a^(2))/(b^(2)), subtend an angle theta at the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then theta=

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