Question

The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation 1 of the ellipse is -

• A. $x^2+2y^2=100$
• B. $x^2+\sqrt{2}{y}^2=10$
• C. $x^2-2y^2=100$
• D. None of these

Answer 1

The correct option is A $x^2+2y^2=100$

ATQ

$2b+2ae+\frac{2b^2}{a}=10\Rightarrow b^2=5a$

$\Rightarrow$ $b=ae$

$\Rightarrow b^2=a^2{e}^2=a^2(1-\frac{b^2}{a^2})$

$\Rightarrow b^2=a^2-b^2\Rightarrow a^2=2b^2$

$\Rightarrow a^2=10a\Rightarrow b^2=50$

thus

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\Rightarrow \frac{x^2}{100}+\frac{y^2}{50}=1\Rightarrow x^2+2y^2=100$