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AP EAMCET202018 Sep 2020Morning ShiftMathematicsEllipseActual

The lengths of the sides of the rectangle of greatest area that can be inscribed in the ellipse (x^2+4 y^2=64 ) are

Options

  1. A(6 2 , 4 2 )
  2. B(8 2 , 4 2 )
  3. C(8 2 , 8 2 )
  4. D(16 2 , 4 2 )

Correct answer

B. (8 2 , 4 2 )

Step-by-step solution

Equation of given ellipse is ( array rlrl & x^2+4 y^2 =64 & x^2 64 + y^2 16 =1 array ) Let the vertex (P(8 , 4 ) ) of the rectangle (P Q R S ) having greatest area. ( aligned Area & =A=4(8 )(4 ) & =64 2 aligned ) For greatest ( area 2 =1 ), so (A=64 ) sq. units and ( = 4 ). Therefore point (P(4 2 , 2 2 ) ) So, length of the sides are (8 2 ) and (4 2 ).

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