Q208 / 270 · NDA 2016 (Phase 2) · Mathematics
If the ellipse $9 x^2+16 y^2=144$ intercepts the line $3 x+4 y=12$, then what is the length of the chord so formed?
- Correct answerA5 units
- B6 units
- C8 units
- D10 units
Solution
Here,
$9 x^2+16 y^2=144$ and $3 x+4 y=12$
$\Rightarrow x=\frac{12-4 y}{3}$
So, $9\left(\frac{12-4 y}{3}\right)^2+16 y^2=144$
On solving we get, $y=0,3$
For $y=0 ; x=4$
For $y=3 ; x=0$
$\begin{aligned}
\Rightarrow \text { Length of chord }= & \sqrt{(0-3)^2+(4-0)^2}=\sqrt{9+16} \\
& =\sqrt{25}=5 \text { units }
\end{aligned}$
Hence, the correct answer is option: 'A'.