A) \[\frac{1}{2}\]
B) \[1\]
C) \[\frac{3}{2}\]
D) \[\frac{5}{2}\]
Correct Answer: D
Solution :
Given,\[\frac{5}{r}=2+3\cos \theta +4\sin \theta \] \[\Rightarrow \] \[\frac{5}{r}=2+5\left( \frac{3}{5}\cos \theta +\frac{4}{5}\sin \theta \right)\] \[\Rightarrow \] \[\frac{5/2}{r}=1+\frac{5}{2}(\cos \phi \cos \theta +\sin \phi \sin \theta )\] \[\left( \text{put}\,\,\cos \phi =\frac{3}{5},\,\,\text{then}\,\,\sin \phi =\frac{4}{5} \right)\] \[\Rightarrow \] \[\frac{5/2}{r}=1+\frac{5}{2}\cos (\theta -\phi )\] It is of the form\[\frac{l}{r}=1+e\cos \theta \] \[\therefore \] \[e=\frac{5}{2}\]
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