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 $m$.