  We study the parameterized complexity of the following fundamental geometric
problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$,
compute their minimum enclosing cylinder. ii) Given two $n$-point sets in
$\Rd$, decide whether they can be separated by two hyperplanes. iii) Given a
system of $n$ linear inequalities with $d$ variables, find a maximum-size
feasible subsystem. We show that (the decision versions of) all these problems
are W[1]-hard when parameterized by the dimension $d$. %and hence not solvable
in ${O}(f(d)n^c)$ time, for any computable function $f$ and constant $c$
%(unless FPT=W[1]). Our reductions also give a $n^{\Omega(d)}$-time lower bound
(under the Exponential Time Hypothesis).
