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IF alpha,beta are the eccentric angles o...

IF `alpha,beta` are the eccentric angles of the extremities of a focal chord of the ellipse `x^2/a^2+y^2/b^2=1`. Then show that `e cos""(alpha+beta)/2=cos""(alpha-beta)/2`

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Knowledge Check

  • If alpha, beta are the eccentric angles of the extremities of a focal chord of the ellipse x^(2)/16+y^(2)/9, " then "tan""alpha/2tan""beta/2=

    A
    `(sqrt(5)+4)/(sqrt(5)-4)`
    B
    `9/23`
    C
    `(sqrt(5)-4)/(sqrt(5)+4)`
    D
    `(8sqrt(7)-23)/9`

  • If alpha and beta are the eccentric angles of the ends of a focal chord of the ellipse then cos^(2)((alpha+beta)/(2))sec^(2)((alpha-beta)/(2)) =

    A
    `(a^(2)+b^(2))/(a^(2))`
    B
    `(a^(2)-b^(2))/(a^(2))`
    C
    `(a^(2))/(a^(2)+b^(2))`
    D
    `(a^(2))/(a^(2)-b^(2))`

  • 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

    A
    `(1+tan(alpha)/(2)tan(beta)/(2))/(1-tan (alpha)/(2)tan (beta)/(2))`
    B
    `(1-tan(alpha)/(2)tan(beta)/(2))/(1+tan (alpha)/(2)tan (beta)/(2))`
    C
    `(tan(alpha)/(2)tan(beta)/(2)+1)/(tan(alpha)/(2)tan (beta)/(2)-1)`
    D
    `(tan(alpha)/(2)tan(beta)/(2)-1)/(tan (alpha)/(2)tan (beta)/(2)+1)`

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