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The sides of the greatest rectangle that...

The sides of the greatest rectangle that can be inscribed in the ellipse ` (x^(2))/(a^(2))+(y^(2))/(b^(2))=1` are

A

`a sqrt(2), b sqrt(2)`

B

`sqrt(a), sqrt(b)`

C

a,b

D

`(a)/(sqrt(2)),(b)/(sqrt(2))`

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The correct Answer is:
A
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Knowledge Check

  • Area of the greatest rectangle that can be inscribed in the ellipse x^2/a^2 + y^2/b^2 = 1 is

    A
    `sqrt(ab)`
    B
    `a//b`
    C
    `2ab`
    D
    `ab`

  • The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

    A
    `pi ab`
    B
    `(pi)/(4)(a^(2)+b^(2))`
    C
    `pi(a+b)`
    D
    `pia^(2)b^(2)`

  • The dimension of the rectangle of maximum area that can be inscribed in the ellipse (x//4)^(2) +(y//3)^(2) =1 are

    A
    `sqrt(8),sqrt(2)`
    B
    `4,3`
    C
    `2sqrt(8),3sqrt(2)`
    D
    `sqrt(2),sqrt(6)`

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