If the tangent to the curve, y= e^x at a point (c, e^c ) and the normal to the parabola, y^2=4 x at the point (1,2) intersect at the same point on…

If the tangent to the curve, $\displaystyle y=\mathrm{e}^x$ at a point (c, $\displaystyle \mathrm{e}^{\mathrm{c}}$ ) and the normal to the parabola, $\displaystyle y^2=4 x$ at the point $\displaystyle (1,2)$ intersect at the same point on the $\displaystyle x$-axis, then the value of c is \_\_\_\_.