MCQ
The equation of the ellipse referred to its axes as the axes of coordinates with latus rectum of length $4$ and distance between foci $4 \sqrt 2$ is-
- A$x^2 + 2y^2 = 24$
- B$2x^2 + y^2 = 24$
- ✓$x^2 + 2y^2 = 16$
- D$2x^2 + y^2 = 16$
✓
Answer
Correct option: C.
$x^2 + 2y^2 = 16$
c
$2 \mathrm{ae}=4 \sqrt{2}$ .......$(1)$
$2 \mathrm{ae}=4 \sqrt{2}$ .......$(1)$
$\frac{2 b^{2}}{a}=4$ .....$(2)$
$b^{2}=a^{2}\left(1-e^{2}\right)$ .....$(3)$
From $(1),(2)$ and $( 3)$
$a=4, b=2 \sqrt{2}$
So, $a^{2}=16, b^{2}=8$
Equation of ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{8}=1$
$\Rightarrow x^{2}+2 y^{2}=16$
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