The point P in the hyperbola focus S is such that the tangent at P, the latus rectum through S and one asymptote are concurrent. Prove that SP is parallel to other asymptote.

The asymptotes of a hyperbola are the diagonals of the rectangle formed by the line drawn through extremities of each axis parallel to the other axis.

From a point G on the transerse axis of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1, GL is drawn perpendicular to one of its asymptotes . Also GP is a normal to the curve at P. Prove that LP is parallel to the conjugate axis.

The normla to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 drawn at an extremity of its latus rectum is parallel to an asymptote. Show that the eccentricity is equal to the square root of (1+sqrt(5))//2.