Question

The equation $x=\frac{e^1+e^{-t}}{2},y=\frac{e^t-e^{-t}}{2};t\in R$ represents

• A. an ellipse
• B. a parabola
• C. a hyperbola
• D. a circle

Answer 1

Answer: (C)

a hyperbola

$x=\frac{e^t+e^{-t}}{2}$ $y=\frac{e^t-e^{-t}}{2}$

$x^2=\frac{e^{2t}+e^{-2t}+1}{4}$ $y^2=\frac{e^{2t}+e^{-2t}-1}{4}$

$x^2-y^2=\frac{e^{2t}+e^{-2t}-e^{2t}-e^{-2t}+2}{4}=\frac{2}{4}$

$x^2-y^2=\frac{1}{2}$

$2x^2-2y^2=1$

This is hyperbola

Option $C$ is correct