Question

find the area region enclosed by ellipse x2+9y2=36

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Equation of the ellipse}$

$\mathsf{x^2+9y^2=36}$

$\underline{\textsf{To find:}}$

$\textsf{Area enclosed by the given ellipse}$

$\underline{\textsf{Solution:}}$

$\boxed{\begin{minipage}{7cm} \\\textsf{Area enclosed by the ellipse}\,\mathsf{\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1}\;\textsf{is}\\\\\mathsf{\pi\,ab}\,\textsf{square units} \end{minipage}}$

$\textsf{Consider,}$

$\mathsf{x^2+9y^2=36}$

$\implies\mathsf{\dfrac{x^2}{36}+\dfrac{y^2}{4}=1}$

$\textsf{Here,}\,\mathsf{a^2=36,\;b^2=4}$

$\implies\mathsf{a=6,\;b=2}$

$\textsf{Area enclosed by the given ellipse}$

$\mathsf{=\pi\,ab}$

$\mathsf{=\pi\,(6)(2)}$

$\mathsf{=12\,\pi}\,\textsf{square units}$

$\underline{\textsf{Answer:}}$

$\textsf{Area enclosed by the given ellipse is}$

$\mathsf{12\,\pi}\,\textsf{square units}$

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