A curve is given parametrically by the equations \[x=4-t^2,\ y=4t.\]

Find the equations of the normals to the curve at the points where the curve meets the \(y\)-axis. Show that these normals meet on the \(x\)-axis.

A curve is given parametrically by the equations \[x=4-t^2,\ y=4t.\]

Find the equations of the normals to the curve at the points where the curve meets the \(y\)-axis. Show that these normals meet on the \(x\)-axis.