Tangents are drawn to the ellipse `x^2/a^2+y^2/b^2=1` at two points whose eccentric angles are `alpha-beta` and `alpha+beta` The coordinates of their point of intersection are

Find 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.

If the tangents to ellipse x^2/a^2 + y^2/b^2 = 1 makes angle alpha and beta with major axis such that tan alpha + tan beta = lambda then locus of their point of intersection 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

Show that the tangent to the ellipse x^2/a^2+y^2/b^2=1 at points whose eccentric angles differ by pi/2 intersect on the ellipse x^2/a^2+y^2/b^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

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

The locus of point of intersection of tangents to an ellipse x^2/a^2+y^2/b^2=1 at two points the sum of whose eccentric angles is constant is

The locus of point of intersection of tangents to an ellipse x^2/a^2+y^2/b^2=1 at two points the sum of whose eccentric angles is constant is

If the tangent at any point of an ellipse x^2/a^2 + y^2/b^2 =1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact then show that the eccentricity ‘e’ of the ellipse is given by the absolute value of cos beta/cos alpha

The tangents from (alpha, beta) to the ellipse x^2/a^2 + y^2/b^2 = 1 intersect at right angle. Show that the locus of the point of intersection of normals at the point of contact of the two tangents is the line ay-betax=0 .