Answer
a. The upper branch of the hyperbola: $x^{2} − y^{2} = 1$
Work Step by Step
a.
$x=\sinh(t)$.....(1)
$y=\cosh(t)$.....(2)
by squaring and subtracting 1 and 2:
$x^{2}-y^{2}=\sinh^{2}(t)-\cosh^{2}(t)=1$
Since $y = \cosh(t)\geq 1$, we have the upper branch of the hyperbola
