Question

The length of the chord intercepted by the ellipse $4x^2+9y^2=1$ on the line $9y=1$ is:

• A. $2\sqrt{2}$
• B. $\frac{2\sqrt{2}}{3}$
• C. $\sqrt{2}$
• D. $3\sqrt{2}$

Answer 1

Answer: (B)

$\frac{2\sqrt{2}}{3}$

Given line is $9y=1$

$\Rightarrow y=\frac{1}{9}$
Solving this line with given ellipse,
$4x^2+9\left(\frac{1}{81}\right)=1$

$\Rightarrow 4x^2=1-\frac{1}{9}=\frac{8}{9}$
$\Rightarrow x^2=\frac{2}{9}$

$\Rightarrow x=\pm \frac{\sqrt{2}}{3}$
Hence required length of chord is $=\frac{\sqrt{2}}{3}-(-\frac{\sqrt{2}}{3})=\frac{2\sqrt{2}}{3}$
Since chord is parallel to x-axis