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

Let P be a variable point on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` with foci `S_(1)andS_(2)`. If A be the area of the triangle `PS_(1)S_(2)`, then the maximum value of A is :

A

ab

B

abe

C

e

D

None of these

Text Solution

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The correct Answer is:
B
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Find the area of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1

Equation of the ellipse is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S_(1) and S_(2) The maximum area of the triangle P S_(1) S_(2) , where P is any point on the ellipse is

Knowledge Check

  • Area of the ellipse x^(2)/9+y^(2)/4=1 is

    A
    `36 pi`
    B
    `6pi`
    C
    6
    D
    none of these

  • The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

    A
    `b^(2)=c^(2) m^(2)+a^(2)`
    B
    `c^(2)=a^(2) m^(2)-b^(2)`
    C
    `a^(2)=b^(2) m^(2)+c^(2)`
    D
    `c^(2)=a^(2) m^(2)+b^(2)`

  • The distance of the point theta^(prime) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 from a focus is

    A
    `a(e+cos theta)`
    B
    ` a(1+e cos theta)`
    C
    ` a(1-e cos theta)`
    D
    `a(1+2 e cos theta)`

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