If the chord through the points whose eccentric angles are α and β on the ellipse `x^2/a^2+y^2/b^2=1` passes through the focus (ae, 0), then the value of `tan(α/2)tan(β/2)` is: A. `(e+1)/(e−1) B. (e−1)/(e+1) C. (e+1)/(e−2)` D. none

If the chord through the points whose eccentric angles are theta and varphi on the ellipse (x^2)/(25)+(y^2)/9=1 passes through a focus, then the value of tan(theta/2)tan(varphi/2) is 1/9 (b) -9 (c) -1/9 (d) 9

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^2 - y^2/b^2 = 1 passes through a focus, prove that tan (theta/2) tan (phi/2) + (e-1)/(e+1) = 0 .

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

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 e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

If alpha and beta are two points on the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 and the chord joining these two points passes through the focus (ae, 0) then e cos ""(alpha-beta)/(2)=

The normal at an end of a latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1 passes through an end of the minor axis if (A) e^4+e^2=1 (B) e^3+e^2=1 (C) e^2+e=1 (D) e^3+e=1

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

the equation of the ellipse passing through (2,1) having e=1/2 , is

If e_1a n d\ e_2 are respectively the eccentricities of the ellipse (x^2)/(18)+(y^2)/4=1 and the hyperbola (x^2)/9-(y^2)/4=1, then write the value of 2e_1^ 2+e_2^ 2dot