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 $(\pm ae,0)$
Since, $x=2y+3$ is a focal chord.
$\therefore$ It passes through foci.
$\Rightarrow ae=2\left(0\right)+3$
$\Rightarrow a=\frac{3}{e}=\frac{3\times 4}{3}=4$
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, $2b=2\sqrt{7}$