Question

vertices of an ellipse are $(0,\pm 10)$ and its eccentricity $e=4/5$ then its equation is

• A. $90x^2-40y^2=3600$
• B. $80x^2+50y^2=4000$
• C. $36x^2+100y^2=3600$
• D. $100x^2+36y^2=3600$

Answer 1

The correct option is D $100x^2+36y^2=3600$

Let the equation of the required ellipse be

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1⟶\left(1\right)$

since the vertices of the ellipse are on $y$-axis, so the coordinate of the vertices are $(0,\pm b)$

$\therefore b=10Now,a^2=b^2(1-e^2)\Rightarrow a^2=100(1-\frac{16}{25})\Rightarrow a^2=36$

substituting the value of $a^2$ and $b^2$ in equation $\left(1\right)$

we get, $\frac{x^2}{36}+\frac{y^2}{100}=1\Rightarrow 100x^2+36y^2=3600\Rightarrow 100x^2+36y^2-3600=0$