If `alpha-beta` is constant prove that the chord joining the points `alpha` and `beta` on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))` =1 touches a fixed ellipse

Find the equation of the chord joining point P(alpha) and Q(beta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.

If alpha,beta are the ends of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then its eccentricity e is

If the chord joining two points whose eccentric angles are alpha and beta cut the major axis of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distance from the centre then tan (alpha)/(2).tan (beta)/(2) =

Find the condition for the line x cos alpha +y sin alpha =p to be a tangent to the ellipse x^2/a^2+y^2/b^2=1 .

The locus a point P ( alpha , beta) moving under the condition that the line y= alpha x+ beta is a tangent to the hyperbola (x^(2))/( a^(2)) -(y^(2))/( b^(2))= 1 is

If the latus rectum of the ellipse x^(2)tan^(2)alpha+y^(2)sec^(2)alpha=1 is 1/2 then alpha=