A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{\sqrt{3}}{4}\]
C) \[\frac{2}{\sqrt{5}}\]
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
\[e=?,\] centre at (0, 0) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\frac{16}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\] \[16{{b}^{2}}+{{a}^{2}}={{a}^{2}}{{b}^{2}}\] ?(1) \[\frac{4}{{{a}^{2}}}+\frac{4}{{{b}^{2}}}=1\] \[4{{b}^{2}}+4{{a}^{2}}={{a}^{2}}{{b}^{2}}\] ?(2) From (1) & (2) \[16{{b}^{2}}+{{a}^{2}}=4{{a}^{2}}+4{{b}^{2}}\] \[3{{a}^{2}}=12{{b}^{2}}\,=\]
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