A) \[\frac{3}{2}\]
B) 2
C) \[\frac{5}{2}\]
D) 3
Correct Answer: B
Solution :
[b] \[y=-2x+1\] passes through \[\left( \frac{a}{e},0 \right)\] \[\therefore \frac{a}{e}=\frac{1}{2}\] \[y=-2x+1\] touches the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\therefore \text{ }1=4{{a}^{2}}-{{b}^{2}}\] \[\Rightarrow 1=4{{a}^{2}}-{{a}^{2}}\left( {{e}^{2}}-1 \right)\] \[\Rightarrow 1=\frac{{{e}^{2}}}{4}\left( 5-{{e}^{2}} \right)\] \[\Rightarrow {{e}^{4}}-5{{e}^{2}}+4=0\] \[\Rightarrow {{e}^{2}}=4,1\] \[\therefore \text{ }{{e}^{2}}\ne 1\therefore \text{ }e=2\]
You need to login to perform this action.
You will be redirected in
3 sec
