Question

Equation of the ellipse whose axes are the axes of coordinatesand which passes through the point (-3,1) and hasaccentricity $\sqrt{\frac{2}{5}}$ is

Answer 1

Let ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

passes thorugh $(-3,1)\frac{9}{a^2}+\frac{1}{b^2}=1.......\left(1\right)$

$e=\sqrt{\frac{2}{5}}$

$\sqrt{1-\frac{b^2}{a^2}}=\sqrt{\frac{2}{5}}\frac{b^2}{a^2}=\frac{3}{5}$

Put in $\left(1\right)$

$\frac{9}{a^{32}}+\frac{5}{3a^2}=1$

$\frac{32}{3a^2}=1a^2=\frac{32}{3}{b}^2=\frac{32}{5}$

Ellipse: $\frac{3x^2}{32}+\frac{5y^2}{32}=1$

$3x^2+5y^2=32$