Conic Sections Question 200
Question: If the ellipse $ 9x^{2}+16y^{2}=144 $ intercepts the line $ 3x+4y=12, $ then what is the length of the chord so formed-
Options:
A) 5 units
B) 6 units
C) 8 units
D) 10 units
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Here, $ 9x^{2}+16y^{2}=144 $ And $ 3x+4y=12 $
$ \Rightarrow x=\frac{12-4y}{3} $ So, $ 9{{( \frac{12-4y}{3} )}^{2}}+16y^{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}=5units $
BETA
