Question

If $x = 2y + 3$ is a focal chord of the ellipse with eccentricity 3/4, then the lengths of the major and minor axes are

• A. $4 , \sqrt{7}$
• B. $8, 2\sqrt{7}$
• C. 6, 4
• D. none of these

Answer 1

Answer: (B)

$x = 2y + 3$ is a focal chord of the ellipse with eccentricity $ \frac{3}{4}$, foci are $(± ae, 0)$
Since, $x = 2y + 3$ is a focal chord.
$\therefore $ It passes through foci.
$\Rightarrow ae =2\left(0\right) + 3 $
$\Rightarrow a= \frac{3}{e} = \frac{3\times4}{3} = 4 $
Now, $b^2 = a^2 (1 -e^2)$
$\Rightarrow b^{2} = \left(4\right)^{2} \left(1 -\left(\frac{3}{4}\right)^{2}\right) = 7 $
$\Rightarrow b- \pm\sqrt{7}$
$ \therefore $ Length of major axis, $2a = 8$ and length of minor axis, $2b = 2 \sqrt{7}$