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Let P be a variable point on the ellipse...

Let P be a variable point on the ellipse with foci `S_(1)` and `S_(2)` . If A be the area of `trianglePS_(1)S_(2)` then find the maximum value of A

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abe
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Knowledge Check

  • P is a variable point on the ellipse x^2/a^2+y^2/b^2=1 with foci F_1 and F_2 . IF A is the area of the triangle PF_1,F_2 , then the maximum value of A is

    A
    `e/(ab)`
    B
    `(ae)/b`
    C
    `(ae)/b`
    D
    `(ab)/e`

  • Let 'P' be a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S (ae , 0) and S'(-ae,0) . If A is the area of the triangle PSS' , then the maximum value of A (where e is eccentricity and b^(2)=a^(2)(1-e^(2))) is

    A
    `(ab)/(2)`
    B
    2 abe
    C
    abe
    D
    4abe

  • P is a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with AA as the major axis. Then the maximum value of the area of triangle APA' is

    A
    ab
    B
    2ab
    C
    `(ab)/(2)`
    D
    `(ab)/(3)`

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