Question

Variable ellipses are drawn with $x=-4$ as directrix and the origin as the corresponding focus. The eccentricity of the locus of the extremities of the minor axes of these ellipses is

• A. $1$
• B. $2$
• C. $\sqrt{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

Now $k=b$ and $h=ae$
Also $\frac{a}{e}-ae=4\Rightarrow a\left(1 - e^{2}\right)=4e$
$\Rightarrow a^{2}\left(1 - e^{2}\right)=4ae$
$\Rightarrow b^{2}=4h$
$\Rightarrow k^{2}=4h\Rightarrow y^{2}=4x$
$\Rightarrow $ eccentricity $=1$