A) an ellipse
B) a circle
C) a pair of straight lines
D) a hyperbola
Correct Answer: D
Solution :
Given equations can be rewritten as \[\frac{x}{a}=t+\frac{1}{t}\] and \[\frac{y}{b}=t-\frac{1}{t}\] On squaring and subtracting, we get \[{{\left( \frac{x}{a} \right)}^{2}}-{{\left( \frac{y}{b} \right)}^{2}}={{\left( t+\frac{1}{t} \right)}^{2}}-{{\left( t-\frac{1}{t} \right)}^{2}}\] \[=\left( {{t}^{2}}+\frac{1}{{{t}^{2}}}+2 \right)-\left( {{t}^{2}}+\frac{1}{{{t}^{2}}}-2 \right)=4\] \[\Rightarrow \frac{{{x}^{2}}}{4{{a}^{2}}}-\frac{{{y}^{2}}}{4{{b}^{2}}}=1\]
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