Auxins are plants hormones. Geotropism and phototropism are caused by unequal growth of plant parts and controlled by auxins.
Effect on phototropism: -
From shoot, auxins pass down to the growing region specially the region of cell elongation to stimulate the growth. So shoots grow upward and show positive phototropic response.
Effect on geotropism: -
The increased concentration of auxins in lower side of root results in movement of root towards force of gravity. So roots grow in earth and show positive geotropic response.