Question
Compare the curves represented by the parametric equations. How do they differ?(a) $x=t, \quad y=t^{-2}$(b) $x=\cos t, \quad y=\sec ^{2} t$(c) $x=e^{t}, \quad y=e^{-2 t}$
Step 1
This is a hyperbola that opens upwards and downwards. The curve is symmetric with respect to the y-axis. As $t$ increases, $x$ increases linearly, but $y$ decreases quadratically. Show more…
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