A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{1}{2}\]
C) \[\frac{\sqrt{3}}{4}\]
D) \[\sqrt{3}\]
Correct Answer: A
Solution :
Given equation of conic is \[4{{x}^{2}}+16{{y}^{2}}-24x-3y=1\] \[\Rightarrow \]\[{{(2x-6)}^{2}}+{{(4y-4)}^{2}}=53\] \[\Rightarrow \]\[4\,{{(x-3)}^{2}}+16\,{{(y-1)}^{2}}=53\] \[\Rightarrow \]\[\frac{{{(x-3)}^{2}}}{53/4}+\frac{{{(y-1)}^{2}}}{53/16}=1\] \[\therefore \] \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1-\frac{53/16}{53/4}}=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}\].
You need to login to perform this action.
You will be redirected in
3 sec
