Question

The length of major and minor axis of an ellipse are $10$ and $8$, respectively, and its major axis lies along the $Y$-axis, then the equation of the ellipse referred to its centre as origin is

• A. $25x^2+16y^2=400$
• B. $\frac{x^2}{16}+\frac{y^2}{25}=1$
• C. $16x^2+25y^2=1600$
• D. $\frac{x^2}{64}+\frac{y^2}{100}=1$

Answer 1

Answer: (A), (B)

The correct options are
A $25x^2+16y^2=400$
B $\frac{x^2}{16}+\frac{y^2}{25}=1$

Given length of major and minor axis of an ellipse are $10$ and $8$.

Thus $b=5$ and $a=4$
Therefore, required equation of ellipse is $\frac{x^2}{(4{)}^2}+\frac{y^2}{(5{)}^2}=1$
$\Rightarrow \frac{x^2}{16}+\frac{y^2}{25}=1$
$\Rightarrow \frac{25x^2+16y^2}{400}=1$
$\Rightarrow 25x^2+16y^2=400$

Hence, options A and B are correct.