Foot of perpendiculars F1 and F2 are drawn to the asymptotes of the hyperbola`x^2/a^2 - y^2/b^2 =1` point P on it. Find the area of the triangle `PF_1F_2`

Foot of perpendiculars F1 and F2 are drawn to the asymptotes of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 point P on it.Find the area of the triangle PF_(1)F_(2)

The product of perpendicular drawn from any points on a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 to its asymptotes is

The product of perpendicular drawn from any points on a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 to its asymptotes is

The product of the perpendicular from any poitn P(x,y) on the hyperbola x^2/a^2 - y^2/b^2 = 1 to its asymptotes is

The product of the perpendicular from any point on the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 to its asymptotes is

From a point G on the transverse axis, GL is drawn perpendicular to the asymptote and GP be a normal to the hyperbola x^2/a^2 - y^2/b^2 = 1 at P . Prove that LP is parallel to the conjugate axis.