Q.Find the

The hyperbola's focal properties mirror the ellipse's closely, but with one sign consistently flipped throughout. The latus rectum again has length $\dfrac{2b^2}{a}$, and the distance between directrices is again $\dfrac{2a}{e}$ — these two formulas are actually identical in form to the ellipse's.

The key DIFFERENCE is in the focal-distance identity: whereas an ellipse point's focal distances always SUM to the constant $2a$, a hyperbola point's focal distances always have DIFFERENCE equal to the constant $2a$ — the length of the transverse axis. This is the hyperbola's own defining "distance" property, the counterpart of the ellipse's pin-and-string construction. …