Search any question & find its solution
Question:
Answered & Verified by Expert
If the ellipse $9 \mathrm{x}^{2}+16 \mathrm{y}^{2}=144$ intercepts the line $3 \mathrm{x}+4 \mathrm{y}=12$. then what is the length of the chord so formed?
Options:
Solution:
1127 Upvotes
Verified Answer
The correct answer is:
5 units
Here,
$9 x^{2}+16 y^{2}=144$ and $3 x+4 y=12$
$\Rightarrow x=\frac{12-4 y}{3}$
$9\left(\frac{12-4 y}{3}\right)^{2}+16 y^{2}=144$
On solving we get, $y=0,3$ For $y=0 ; x=4$
For $y=3 ; x=0$
$\Rightarrow$ Length of chord $=\sqrt{(0-3)^{2}+(4-0)^{2}}=\sqrt{9+16}$
$=\sqrt{25}=5$ units
$9 x^{2}+16 y^{2}=144$ and $3 x+4 y=12$
$\Rightarrow x=\frac{12-4 y}{3}$
$9\left(\frac{12-4 y}{3}\right)^{2}+16 y^{2}=144$
On solving we get, $y=0,3$ For $y=0 ; x=4$
For $y=3 ; x=0$
$\Rightarrow$ Length of chord $=\sqrt{(0-3)^{2}+(4-0)^{2}}=\sqrt{9+16}$
$=\sqrt{25}=5$ units
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.