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

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

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

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 .

If the tangent at any point of the ellipse (x^2)/(a^3)+(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 of the ellipse is given by e=cosbeta/(cosalpha)

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

The tangent at the point alpha on the ellipse x^2/a^2+y^2/b^2=1 meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity 'e' of the ellipse is given by the equation (A) e^2(1+cos^2alpha)=1 (B) e^2(cosec^2alpha-1)=1 (C) e^2(1+sin^2alpha)=1 (D) e^2(1+tan^2alpha)=1