The focal distances SP = a - ex1 and SP' = a + ex1 sum to 2a. For a focal chord (chord through a focus), the endpoints have eccentric angles satisfying tan$\frac{alpha}{2}$tan$\frac{beta}{2}$ = $\frac{e-1}{(e+1)}$. The minimum focal chord is the latus rectum = 2$b^2$/a, occurring when the chord is perpendicular to the major axis. The harmonic mean of the two focal segment lengths equals the semi-latus rectum $b^2$/a. The circle on a focal chord as diameter touches the corresponding directrix. If d1 and d2 are perpendicular distances from foci to any tangent, then d1d2 = $b^2$. The segment TG (tangent and normal meet the axis at T and G) subtends a right angle at either focus. These focal properties are the most frequently tested in JEE, especially SP + SP' = 2a.