[" If "alpha,beta" are the ends of a fo- "],[" cal chord of the ellipse "],[(x^(2))/(a^(2))+(y^(2))/(b^(2))=1," then its eccentri- "],[" city e is "]

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

Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentricity e is

IF alpha , beta are eccentric angles of end points of a focal chord of the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 then tan(alpha /2) tan (beta/2) is equal to

Show that the tangents at the end of any focal chord of the ellipse x^(2)b^(2)+y^(2)a^(2)=a^(2)b^(2) intersect on the directrix.

The length of the Latusrectum of the ellipse ((x-alpha)^(2))/(a^(2))+((y-beta)^(2))/(b^(2))=1 (a

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

If the polar with respect to y^(2)=4ax touches the ellipse (x^(2))/(alpha^(2))+(y^(2))/(beta^(2))=1, the locus of its pole is

Locus of the point of intersection of the tangent at the ends of focal chord of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , (b lt a) is

If (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .