The paraboloid $z=8-x-x^2-3y^2$ intersects the plane $x=4$ in a parabola. Find parametric equations in terms of $t$ for the tangent line to this parabola at the point $(4,2,-24).$ Use a computer to graph the paraboloid, the parabola, and the tangent line on the same screen. $($Enter your answers as comma$-$separated lists of equations. Use $t$ as your parameter.$)$