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

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

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

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 angle beta with the focal radius of the point of contact,then show that the eccentricity of the ellipse is given by e=cos(beta)/(cos alpha)

If the tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angles alpha and beta with the major axis such that tan alpha+tan beta=gamma ,then the locus of their point of intersection is x^(2)+y^(2)=a^(2)(b)x^(2)+y^(2)=b^(2)x^(2)-a^(2)=2 lambda xy(d)lambda(x^(2)-a^(2))=2xy

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

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

Two tangents drawn on parabola y^(2)=4ax are making angle alpha_ _(1)and alpha_(2), with y -axis and if alpha_(1)+alpha_(2)=2 beta then locus of the point of intersection of these tangent 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

Point of intersection of tangents at P(alpha) and Q(Beta)