Question

Solve : $area\:\frac{\left(x-1\right)^2}{9}+\frac{y^2}{5}=100$

Answer 1

$\bf{Ellipse\:Area\:given}\:\frac{\left(x-1\right)^2}{9}+\frac{y^2}{5}=100:\quad A=300\sqrt{5}\pi$

$A=\pi \cdot \:a\cdot \:b$

$\frac{\left(x-1\right)^2}{9}+\frac{y^2}{5}=100:\quad \mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(1,\:0\right),\:\mathrm{semi-major\:axis}\:a=30,\:\mathrm{semi-minor\:axis}\:b=10\sqrt{5}$

$\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1\:\mathrm{is\:the\:ellipse\:standard\:equation}$

$\mathrm{Rewrite}\:\frac{\left(x-1\right)^2}{9}+\frac{y^2}{5}=100\:\mathrm{in\:the\:form\:of\:the\:standard\:ellipse\:equation}$

$\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(1,\:0\right),\:\:\mathrm{semi-major\:axis}\:a=30,\:\:\mathrm{semi-minor\:axis}\:b=10\sqrt{5}$

$A=\pi 30\cdot \:10\sqrt{5}$

$\mathrm{Refine}$

$A=300\sqrt{5}\pi$