Similarity and congruence of plane curves

Prove that the curves $r = e^{a\varphi }$ and $r = ce^{a\varphi }$ are geometrically similar — one is transformed into the other by enlarging the scale of the drawing. At the same time they are congruent, transforming into each other under a rotation through a certain angle.

Prove that the figures enclosed between the $x$-axis and the curves $y = e^{x}$ and $y = ae^{x}$ can be made to coincide by translating one of these curves along the $x$-axis.