A) an ellipse
B) a parabola
C) a hyperbola
D) a circle
E) none of these
Correct Answer: C
Solution :
\[\because \]\[x=\frac{{{e}^{t}}+{{e}^{-t}}}{2}\]and\[y=\frac{{{e}^{t}}-{{e}^{-t}}}{2}\] \[\because \] \[{{({{e}^{t}}+{{e}^{-t}})}^{2}}={{({{e}^{t}}-{{e}^{-t}})}^{2}}+4\] \[\Rightarrow \]\[\frac{{{({{e}^{t}}+{{e}^{-t}})}^{2}}}{4}=\frac{{{({{e}^{t}}-{{e}^{-t}})}^{2}}}{4}+1\] \[\Rightarrow \]\[{{x}^{2}}={{y}^{2}}+1\Rightarrow {{x}^{2}}-{{y}^{2}}=1\] This shows the given equation represents a hyperbola.
You need to login to perform this action.
You will be redirected in
3 sec
