Question

Equation of the ellipse with foci ($\pm ,0$) and e = $\frac{1}{4}$ is

• A. $\frac{x^2}{16}+\frac{y^2}{14}$ = 1
• B. $\frac{x^2}{18}+\frac{y^2}{16}$ = 1
• C. $\frac{x^2}{20}+\frac{y^2}{18}$ = 1
• D. $\frac{x^2}{32}+\frac{y^2}{30}$ = 1

Answer 1

The correct option is D

$\frac{x^2}{32}+\frac{y^2}{30}$ = 1

S = ($\pm \sqrt{2},0$), e =$\frac{1}{4}$

C = (0,0), $b^2$ = $32\left(\frac{15}{16}\right)$ = 30

ae = $\sqrt{2}$

a = $4\sqrt{2}$,
$\frac{x^2}{32}+\frac{y^2}{30}$ = 1