The curve with equation
$6{e^{2x}} + k{e^y} + {e^{2y}} = c$
where $k$ and $c$ are constants, passes through the point $P$ with coordinates (ln 3, ln 2).
a) Show that $58 + 2k = c$.
b) Given also that the gradient of the curve at $P$ is $ - 6$, find the values of $k$ and $c$.