If the chord, joining two points whose eccentric angles are `alpha and beta`, cuts the major axis ofthe ellipse `x^2/a^2 + y^2/b^2=1` at a distance c from the centre, then `tan alpha//2.tan beta//2` is equal to

The length ofthe normal (terminated by the major axis) at a point of the ellipse x^2/a^2+y^2/b^2=1 is

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

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 subtends a right angle at the vertex A(a ,0), then prove that tan(a/2)tan(beta/2)=-(b^2)/(a^2)dot

If sin alpha + sin beta=a and cos alpha+cosbeta=b then tan((alpha-beta)/2) is equal to

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

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

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

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/2) is equal to-

If any two chords be drawn through two points on the major axis of the ellipse x^2/a^2+y^2/b^2=1 equidistant from the centre. If α,β,γ,δ are the eccentric angles of the extremities of the chords, then the value of tan(α/2)tan(β/2)tan(γ/2)tan(δ/2) , is

If cos alpha=(2cos beta-1)/(2-cos beta) then tan (alpha/2) is equal to