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

Length of the major axis of the ellipse 9x^(2)+7y^(2)=63, is

If the normal at P(theta) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 with focus S ,meets the major axis in G. then SG=

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

The locus of the mid-points of the chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which pass through the positive end of major axis,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

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is