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)`

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

Length of the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which is inclined to the major axis at angle theta is

If the tangents from the point (lambda,3) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 are at right angles then lambda is

If the tangents drawn from a point on the hyperbola x^(2)-y^(2)=a^(2)-b^(2) to ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angle alpha and beta with the transverse axis of the hyperbola, then

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 points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 such that the tangent at each point makes equal angles with the axes.

If the distance of a point on the ellipse (x^(2))/(6) + (y^(2))/(2) = 1 from the centre is 2, then the eccentric angle of the point, is

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is