2001 TYS

Find the equation of the tangent to the curve \(y={{e}^{x}}\) at the point where \(x=a\). Hence find the equation of the tangent to the curve \(y={{e}^{x}}\) which passes through the origin. The straight line \(y=mx\) intersects the curve \(y={{e}^{x}}\) in two distinct points. Write down an inequality for \(m\).