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Area of the greatest rectangle inscribed...

Area of the greatest rectangle inscribed in the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` is:

A

24

B

12

C

144

D

`sqrt(24)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

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

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

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

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

  • The area of the directrix circle of the ellipse (x^(2))/(16)+(y^(2))/(9)=1 is:

    A
    `25pi`
    B
    `10pi`
    C
    `15pi`
    D
    `5pi`

    • Similar Questions

    Explore conceptually related problems

    Find the area of the region bounded by the ellipse (x^(2))/(16) + (y^(2))/(9) = 1

    Find the area of the greatest isosceles triangle that can be inscribed in the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 having its vertex coincident with one extremity of the major axis.

    Find the area of the region bounded by the ellipse (x^(2))/(4) + (y^(2))/(9) = 1

    Find the area of the smaller region bounded by the ellipse (x^(2))/(9) + (y^(2))/(4) = 1 and the line (x)/(3) + (y)/(2) = 1

    The maximum area of an isosceles triangle inscribed in the ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 with the vertex at one end of the major axis is

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