Question

If the centre, one of the foci and semi-major axis of an ellipse be $(0,0),(0,3)$ and $5$, then its equation is:

• A. $\frac{x^2}{16}+\frac{y^2}{25}=1$
• B. $\frac{x^2}{25}+\frac{y^2}{16}=1$
• C. $\frac{x^2}{9}+\frac{y^2}{25}=1$
• D. none of these

Answer 1

Answer: (A)

$\frac{x^2}{16}+\frac{y^2}{25}=1$

Given centre $(0,0)$, focus $(0,3),b=5$
$\Rightarrow be=3\Rightarrow e=\frac{3}{5}$
$\therefore a=b\sqrt{1-e^2}=5\sqrt{1-\frac{9}{25}}=4$
Hence, required equation is
$\frac{x^2}{16}+\frac{y^2}{25}=1$