Question

$(-4,1),(6,1)$ are the vertices of an ellipse and one of the foci lies on $x-2y=2$ then the eccentricity is

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{2}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{3}{5}$

Given, $(-4,1)$ and $(6,1)$ are vertices of an ellipse.
$\Rightarrow$ Major axis of ellipse is $y=1$

Centre of ellipse is $(1,1)$

Foci are $x=2+2y=2+2=4$
$\therefore$ Focus is $(4,1)$

$\because$ Focus lies on major axis.
$\therefore ae=$ Distance b/w focus and centre $=3$
$a=\frac{10}{2}=5$

$\Rightarrow e=\frac{3}{5}$

Hence, option A.