Find the maximal possible area for a rectangle inscribed in the ellipse 16x^2 + 9y^2 = 144.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The maximal possible area for a rectangle inscribed in the ellipse 16x^2 + 9y^2 = 144 has to be found.

First convert the equation of the ellipse to the form: `x^2/a^2 + y^2/b^2 = 1`

16x^2 + 9y^2 = 144

=> `(16x^2)/144 + (9y^2)/144 = 1`

=>`x^2/(144/16) + y^2/(144/9) = 1`

=> `x^2/3^2 + y^2/4^2 = 1`

The area of the largest rectangle that can be fit into an ellipse `x^2/a^2 + y^2/b^2 = 1` is equal to 2*a*b

Here it is 2*3*4 = 24

The required area of the largest rectangle that can be inscribed in the ellipse 16x^2 + 9y^2 = 144 is 24

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