Abstract: This paper uses analytical geometry and analytical mechanics to obtain the conditions of a homo-geneous slender rod in a state of balance and in the stable equilibrium when it is in the inner wall of a smooth conic curve , as well as the static properties of the conic curve. When the homogeneous slender rod goes through the focus and is in the inner wall of a smooth conic curve aslant, the homogeneous slender rod will be in a state of stable equilibrium. Its mechanical properties are also proven by using its optical properties.