A) a circle
B) an ellipse
C) a hyperbola
D) a parabola
Correct Answer: C
Solution :
Given parametric equations are \[x={{e}^{t}}+{{e}^{-t}}\] and \[y={{e}^{t}}-{{e}^{-t}},\] now squaring and subtracting, we get \[{{x}^{2}}-{{y}^{2}}={{e}^{2t}}+{{e}^{-2t}}+2{{e}^{t-t}}\] \[-({{e}^{2t}}+{{e}^{-2t}}-2{{e}^{t-t}})\] \[\Rightarrow \] \[{{x}^{2}}-{{y}^{2}}=4\] \[\Rightarrow \] \[{{x}^{2}}-{{y}^{2}}=4\] Which is the equations of a hyperbola.
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